Types of Numbers, Factors and Multiples PDF

FOR ONLINE USE ONLY DO NOT DUPLICATE Chapter Seven Types of numbers, factors and multiples of numbers Introduction In this chapter, you will learn about types of whole numbers, namely, even...

FOR ONLINE USE ONLY DO NOT DUPLICATE Chapter Seven Types of numbers, factors and multiples of numbers Introduction In this chapter, you will learn about types of whole numbers, namely, even LY numbers, odd numbers and prime numbers. You will also learn about factors and multiples of numbers. You will be able to use factors and multiples in N finding the Greatest Common Factor (GCF) and the Lowest Common Multiple O (LCM) of whole numbers. This competence will help you in comparing prices, exchanging money, dividing things into equal parts, understanding time and measuring quantities of different items. SE Types of numbers U Counting numbers In our daily life, we normally count things. In counting, we start with 1 followed by 2, 3, 4, and so on. The numbers 1, 2, 3, 4, … are known as counting E numbers. They are also called natural numbers. N Example 1 LI List all the counting numbers between 8 and 20. N O Solution The counting numbers between 8 and 20 are 9, 10, 11, 12, 13, 14, 15, R 16, 17, 18, and 19. FO Whole numbers If 0 is included in the set of counting numbers, then we get whole numbers. Therefore, the list of whole numbers is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,... 94 MATH std 5.indd 94 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Example 2 List the first nine whole numbers. Solution The first nine whole numbers are: 0, 1, 2, 3, 4, 5, 6, 7 and 8. LY Even numbers N Even numbers are whole numbers which are exactly divisible by 2. That is, when this number is divided by 2, the remainder is 0. The last digit of an even O number is either 0, 2, 4, 6 or 8. Zero is an even number. SE Activity 1: Identification of even numbers Steps: U 1. List the counting numbers from 1 up to 12. The numbers are 1, 2, 3,4,5,6, 7,8,9,10,11, 12. 2. Represent the numbers by counters as shown in the following table. E N Numbers 1 2 3 4 5 6 7 8 9 10 11 12 Counter LI N O 3. Collect the counters in groups of two and use a line to connect each group. R Numbers 1 2 3 4 5 6 7 8 9 10 11 12 FO Counter 95 MATH std 5.indd 95 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 4. The numbers which have an exact number of groups of two without a remainder are: 2, 4, 6, 8, 10 and 12. These numbers are even numbers. Example 1 List all even numbers between 17 and 33. LY Solution N The even numbers between 17 and 33 are 18, 20, 22, 24, 26, 28, 30 and 32. O Example 2 SE Fill in the blanks with four even numbers that follow in the following pattern of numbers: 574, 572, 570, ____, ____, ____, ____ U Solution Since the pattern is decreasing by 2 at each stage, the next four even numbers are 568, 566, 564 and 562. E N Exercise 1 LI Answer the following questions: 1. List all the even numbers between: N (a) 25 and 35. O (b) 50 and 60. (c) 81 and 99. R 2. Identify and write the even numbers in the following numbers: FO (a) 43, 52, 56, 59, 60. (b) 71, 78, 82, 83, 87. (c) 92, 97, 96, 98, 99. 96 MATH std 5.indd 96 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 3. Which among the following numbers are not even numbers? (a) 52, 55, 56, 57, 59, 60, 62. (b) 18, 33, 36, 37, 40, 58, 70. 4. Write the missing even numbers in the following pattern: 22, 24, 26, _____, _____, _____. LY 5. How many even numbers are there between 45 and 63? N 6. Write all even numbers between 73 and 93 which are exactly divisible by 4. O 7. Write the missing even numbers in the following pattern: SE 30, ____, 34, 36, ____, ____, 42, ____, 46. U Odd numbers Odd numbers are whole numbers which are not divisible by 2. E Activity 2: Identification of odd numbers N Steps: LI 1. List the counting numbers from 1 to 12. The numbers are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. N 2. Represent the numbers by counters. O Numbers 1 2 3 4 5 6 7 8 9 10 11 12 R Counter FO 97 MATH std 5.indd 97 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 3. Collect counters in groups of two and use a line to connect each group. Numbers 1 2 3 4 5 6 7 8 9 10 11 12 Counter LY 4. In step 3, you observe that some numbers have an exact number of N groups of two while others have 1 as remainder. The numbers which have 1 as a remainder are: 1, 3, 5, 7, 9 and 11. These are the odd O numbers. Example 1 SE U Write all odd numbers among the following numbers 38, 49, 87, 96, 105, 254 and 281. E Solution N The odd numbers among the given numbers are: 49, 87, 105 and 281. LI Example 2 N O Write the three missing odd numbers in the following pattern: 1003, 1005, 1007, ______, ______, ______. R Solution FO The missing odd numbers are: 1009, 1011 and 1013. 98 MATH std 5.indd 98 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Exercise 2 Answer the following questions: 1. Given the following list of numbers: 4, 5, 8, 11, 13, 14, 16, 19, 21, 22, 25, 27, 29, 31, 32, 34, 35 (a) Write all odd numbers in the list. (b) Write all odd numbers in the list lying between 8 and 22. LY 2. Write down the missing odd numbers in the following pattern: 9, 11, 13, ____, 17, ____, ____, ____, 25, 27, ____, ____ N 3. How many odd numbers are there among the first 10 counting numbers? O 4. Answer with ‘YES’ or ‘NO’: SE (a) 243 is an odd number. __________ (b) The sum of any two odd numbers is an even number. _________ (c) 2 018 is an odd number. _________ U (d) 999 997 is an odd number. _________ 5. List all odd numbers between 31 and 50 that are exactly divisible by 5. E N Prime numbers LI A prime number is a whole number that is divisible by 1 and itself. It has exactly two factors, that is, one and itself. N O One (1) is not a prime number because it has a single factor which is itself. Activity 3: Identification of prime numbers R FO Prime numbers can be identified using factors. Use the following steps to identify prime numbers. 99 MATH std 5.indd 99 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Steps: 1. List the counting numbers from 1 up to 100. The counting numbers from 1 up to 100 are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, …100. LY 2. Encircle 2, then mark all numbers divisible by 2 with ×. 3. Encircle 3, then mark all numbers divisible by 3 with ×. N 4. Encircle 5, then mark all numbers divisible by 5 and have not been marked with ×. O 5. Encircle 7, then mark all numbers divisible by 7 and have not been marked with ×. SE 6. Encircle 11, then mark all numbers divisible by 11 and have not been marked with ×. 7. Except for the number 1, write all the numbers which have been encircled U and those which have not been marked with x. There are twenty-five (25) such numbers. Those numbers are the prime numbers and they are listed below: E 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, N 61, 67, 71, 73, 79, 83, 89 and 97. LI Example 1 N List all the prime numbers less than 20. O Solution The prime numbers less than 20 are: R 2, 3, 5, 7, 11, 13, 17 and 19. FO 100 MATH std 5.indd 100 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Example 2 Write all the prime numbers between 101 and 120. Steps: 1. List all numbers between 101 and 120. The numbers are: 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119. 2. Mark all numbers that are divisible by 2 with x. This leaves the LY numbers 103, 105, 107, 109, 111, 113, 115, 117 and 119 unmarked. N 3. Mark all numbers listed in Step 2 that are divisible by 3 with x. This leaves the numbers 103, 107, 109, 113, 115 and 119 unmarked. O 4. Mark all numbers listed in Step 3 that are divisible by 5 with x. This leaves the numbers 103, 107, 109, 113 and 119 unmarked. 5. Mark all numbers listed in Step 4 that are divisible by 7 with x. This SE leaves the numbers 103, 107, 109 and 113 unmarked. Thus, the prime numbers between 101 and 120 are: U 103, 107, 109 and 113. Example 3 E Write the prime numbers among the following numbers: N 19, 21, 29, 37, 44, 45, 49, 51, 55, 57 and 59. LI Solution The prime numbers among the given numbers are: N 19, 29, 37 and 59. O Exercise 3 R Answer the following questions: FO 1. Write all the prime numbers among the following numbers: 4, 7, 10, 12, 13, 15, 16, 17. 2. List three prime numbers between 14 and 25. 101 MATH std 5.indd 101 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 3. Identify and write all prime numbers among the following numbers: 123, 125, 127, 128, 130, 131, 135, 137, 138, 139, 142. 4. Write a prime number which is also an even number. 5. How many prime numbers are there between 10 and 20? 6. Think of a prime number such that if you subtract a certain even number from it, the answer is zero. What number is that? LY 7. Find the sum of prime numbers between 1 and 20. N 8. Write the missing prime numbers in the following pattern of prime numbers: 31, _____, _____, _____, 47. O 9. Write all the prime numbers from the following list of numbers: 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95. SE 10. Write ‘TRUE’ or ‘FALSE’ against each of the following statements: (a) All odd numbers are prime numbers. _____ (b) 2 is the smallest prime number. _____ U (c) 1, 2, 3, 4, 5 is a list of prime numbers. _____ (d) 15 is not a prime number. _____ (e) 1 is a prime number. _____ E Factors of a number N A factor of a given number is any number which divides that number without a remainder. The plural of a factor is factors. LI Example 1 N Find all the factors of 6. O Solution R Divide 6 by 1, 2, 3, 4, 5 and 6. 6 ÷ 1= 6, 6 ÷ 4 = 1 with remainder 2, FO 6 ÷ 2 = 3, 6 ÷ 5 = 1 with remainder 1, 6 ÷ 3 = 2, 6 ÷ 6 = 1. The numbers which divide 6 without remainder are 1, 2, 3 and 6. Therefore, the factors of 6 are 1, 2, 3 and 6. 102 MATH std 5.indd 102 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Example 2 List all factors of 36 which are divisible by 2. Solution Find all the factors of 36. Divide 36 by 1, 2, 3, 4, 6, 9, 12, 18 and 36: 36 ÷ 1 = 36, 36 ÷ 9 = 4, 36 ÷ 2 = 18, 36 ÷ 12 = 3, LY 36 ÷ 3 = 12, 36 ÷ 18 = 2, 36 ÷ 4 = 9, 36 ÷ 36 = 1. N 36 ÷ 6 = 6, O The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18 and 36. The factors which are divisible by 2 are: 2, 4, 6, 12, 18 and 36. SE Remark: A number can be written as a product of more than two factors. For example: U 36 E 18 N 2 LI N 9 2 O 3 3 R FO In order to express 36 as a product of prime numbers, multiply all the prime numbers from the tree diagram. That is, ​36  =  2  ×  2  ×  3  ×  3​. 103 MATH std 5.indd 103 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Example 3 Find all the factors of 45. Solution Express 45 as a product of two numbers in different ways. 1 × 45 = 45. Therefore, 1 and 45 are factors of 45. LY 3 × 15 = 45. Therefore, 3 and 15 are factors of 45. 5 × 9 = 45. Therefore, 5 and 9 are factors of 45. N Therefore, the factors of 45 are 1, 3, 5, 9, 15, and 45. O Exercise 4 Answer the following questions: SE 1. Write all the factors of the following numbers: U (a) 20 (b) 7 (c) 12 (d) 5 E 2. Find all the factors of the following numbers: N (a) 8 (b) 16 (c) 24 (d) 49 LI (e) 10 (f) 81 N 3. Fill in the boxes with the missing factors: O (a) 40 = 2 × ×5 (b) 72 = 1 × 2 × 3 × (c) 100 = 2 × × 10 R (d) 90 = 3 × × 6 FO (e) 56 = × 4×7 104 MATH std 5.indd 104 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 4. Fill the missing factors in the following tree diagrams: (a) (b) 30 60 2 15 30 3 LY 2 N (c) O 51 3 5 3 SE U Finding factors of a number by using prime numbers E Prime numbers can also be identified by using tree diagrams. N Activity 4: Identification of prime numbers LI Steps: N 1. List all counting numbers from 1 to 15 and encircle them as follows: O R 1 2 3 4 5 6 7 8 9 10 11 FO 12 13 14 15 105 MATH std 5.indd 105 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 2. Write factors of each number and represent them using branches as shown below: 1 1 2 1 3 1 2 1 5 1 2 3 4 5 1 1 2 1 3 1 4 2 1 5 1 2 3 4 5 LY 1 2 1 7 1 2 1 3 1 2 6 7 8 9 4 10 1 13 62 1 2 7 14 1 8 23 1 9 3 2 115 10 52 16 83 10 5 N 1 2 7 1 49 2 1 11 2 1 13 1 3 3 11 6 12 4 13 8 14 9 4 5 15 10 O 3 12 1 2 11 4 1 2 17 3 142 15 2 1 11 6 72 1 13 153 6 11 12 7 8 13 9 14 10 15 3 12 3 1 6 11 1 4 12 6 2 4 1 8 13 SE 7 1 9 14 14 2 5 1 15 10 15 3 11 13 3 12 U 4 6 7 14 5 15 E 3. List all the numbers in step 2 which have only two factors, that is, N numbers with only two branches. LI The numbers with two branches are 2, 3, 5, 7, 11 and 13. These numbers have only two factors which are 1 and the number itself. Thus, these are N the prime numbers. O Exercise 5 R Find the prime factors of each of the following numbers: FO (a) 12 (b) 28 (c) 15 (d) 24 (e) 14 106 MATH std 5.indd 106 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Greatest common factor The Greatest Common Factor (GCF) is the largest number which divides two or more numbers without a remainder. In other words, the GCF is the largest factor of two or more numbers. Example 1 LY Find the common factors of 6 and 8. N Solution List the factors of 6 and 8: O The factors of 6 are 1, 2, 3 and 6. The factors of 8 are 1, 2, 4 and 8. SE Therefore, the common factors of 6 and 8 are 1 and 2. Example 2 U Find the GCF of 30 and 42. E Solution N The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. LI The common factors of 30 and 42 are 1, 2, 3 and 6. The greatest common factor (GCF) of 30 and 42 is 6. N O Example 3 R Find the GCF of 12 and 18 by using prime factors. FO Solution Recall that a prime number is one among the numbers. 107 MATH std 5.indd 107 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 2, 3, 5, 7, 11, 13, 17…, whose factors are 1 and the number itself. Express 12 as a product of prime numbers: 12 = 2 × 2 × 3. Express 18 as a product of prime numbers: 18 = 2 × 3 × 3. The common prime factors of both numbers are 2 and 3. The product of 2 and 3 is 6. Therefore, the GCF of 12 and 18 is 6. Example 4 LY Find the GCF of 24 and 60 by prime factors. N Solution O 2 24 60 24 and 60 are divisible by 2 2 12 30 12 and 30 are divisible by 2 2 3 5 6 3 1 15 15 5 SE 2 is a factor of 6 but not of 15 3 and 15 are divisible by 3 5 is divisible by 5 U 1 1 When 1 is reached, the process ends The common prime factors of 24 and 60 are 2, 2 and 3. Their product is 2 × 2 × 3 = 12. E N Therefore, the GCF of 24 and 60 is 12. LI Exercise 6 Answer the following questions: N 1. Use listing method to find the common factors of the following pairs of numbers: O (a) 10 and 12 (b) 8 and 16 (c) 15 and 27 (d) 96 and 36 (e) 42 and 72 (f) 7 and 15 R (g) 20 and 21 (h) 18 and 45 (i) 3 and 7 FO 2. Use prime factors to find the GCF of the following pairs of numbers: (a) 11 and 42 (b) 15 and 20 (c) 30 and 90 (d) 8 and 24 (e) 4 and 8 (f) 16 and 24 (g) 12 and 16 108 MATH std 5.indd 108 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 3. Use the method of tree diagram to find the GCF of the following pairs of numbers: (a) 42 and 48 (b) 33 and 72 (c) 72 and 144 (d) 75 and 80 4. Use common prime factors to find the GCF of the following pairs of numbers: (a) 23 and 5 (b) 24 and 156 (c) 24 and 180 LY (d) 35 and 245 (e) 36 and 162 Multiples of numbers N If any counting number is multiplied by another counting number, then the result is called a multiple. The plural of multiple is multiples. O 12 × 1 = 12; 12 is a multiple of 1 and 12. 12 × 2 = 24; 24 is a multiple of 2, 12, and 24. 12 × 3 = 36; 36 is a multiple of 3, 12, and 36. SE Multiples of a number can be listed although the list has no end unless a limit is given. U Example 1 E Write the first five multiples of 2. N Solution LI In order to get the first five multiples of 2, multiply 2 by 1, then by 2, 3, 4 and 5 as follows: N 2 × 1 = 2, 2 × 2 = 4, O 2 × 3 = 6, 2 × 4 = 8, R 2 × 5 = 10. FO Therefore, the first five multiples of 2 are 2, 4, 6, 8 and 10. 109 MATH std 5.indd 109 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Example 2 Write the multiples of 5. Solution The multiples of 5 are obtained by multiplying 5 by 1, then by 2, 3, 4 and so on as follows: 5 × 1 = 5, 5 × 4 = 20, LY 5 × 2 = 10, 5 × 5 = 25, 5 × 3 = 15, 5 × 6 = 30.and so on. N Therefore, the multiples of 5 are 5, 10, 15, 20, 25… O Example 3 SE Use a number line to show the multiples of 3. Solution U 1. Draw a number line as shown below: E 0 1 2 3 4 5 6 7 8 9 10 N 2. Starting from 0 move three successive steps to the right to get 3, 6, LI 9 and so on. N O 0 1 2 3 4 5 6 7 8 9 10 R FO Therefore, the multiples of 3 are 3, 6, 9, 12, 15 and so on. 110 MATH std 5.indd 110 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Exercise 7 Answer the following questions: 1. Write all the multiples of 4 between 2 and 30. 2. Write all the multiples of 11 between 9 and 45. 3. List the first ten multiples of 9. LY 4. Write all the multiples of 7 between 45 and 100. N 5. List all the multiples of the following numbers which do not exceed 60: O (a) 5 (b) 8 (c) 10 (d) 17 SE 6. List all multiples of 6 between 5 and 62. 7. Use the following number line to answer the questions that follow: U 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 E (a) Circle the multiples of 5. N (b) Mark all multiples of 2 by x. LI (c) List the first 5 multiples of 1. N Lowest common multiple The Lowest Common Multiple (LCM) of two or more numbers is the smallest O whole number which is a multiple of those numbers. It is the smallest common multiple of the given numbers. R Example 1 FO List the common multiples of 3 and 6. 111 MATH std 5.indd 111 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Solution Write the multiples of 3. The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, … Write the multiples of 6. The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, … Find the multiples of 3 that are also multiples of 6. The common multiples of 3 and 6 are 6, 12, 18, 24, … LY Therefore, the common multiples of 3 and 6 are: 6, 12, 18, 24, … N Example 2 O Find the lowest common multiple (LCM) of 3 and 4. Solution SE 1. Write the multiples of 3. U The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, … 2. Write the multiples of 4. The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, … E 3. The common multiples of 3 and 4 are 12, 24, … N Therefore, the LCM of 3 and 4 is 12. LI When finding the LCM by using the method of prime factor divisors, all N the prime factor divisors are multiplied. O Example 3 R FO Use the method of common divisors to find the LCM of 12 and 20. 112 MATH std 5.indd 112 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Solution 2 12 20 12 and 20 are divisible by 2 2 6 10 6 and 10 are divisible by 2 3 3 5 3 divides only 3 but not 5 5 1 5 5 divides 5 1 1 When 1 is reached, the process ends LY The lowest common multiple of 12 and 20 is the product of 2 × 2 × 3 × 5 = 60. N Therefore, the LCM of 12 and 20 is 60. O Example 4 SE Find the LCM of 8 and 30 using the method of prime factor divisors. Solution U 2 8 30 2 4 15 2 2 15 E 3 1 15 N 5 1 5 1 1 LI The lowest common multiple of 8 and 30 is the product of 2 × 2 × 2 × 3 × 5 = 120. N O Therefore, the LCM of 8 and 30 is 120. Exercise 8 R FO Answer the following questions: 1. List all multiples of 9 between 20 and 60. 113 MATH std 5.indd 113 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 2. Write all multiples of 5 between 30 and 47. 3. List all common multiples of 5, 8, and 20 between 10 and 100. 4. List the first 5 multiples of each of the following numbers: (a) 6 (b) 35 (c) 13 (d) 24 LY 5. Find the LCM of the following pairs of numbers: (a) 5 and 7 (b) 12 and 40 N (c) 8 and 12 (d) 6 and 13 O 6. Find the LCM of the following pairs of numbers using product of prime numbers: (a) 18 and 30 (d) 25 and 85 (b) 45 and 60 SE (c) 23 and 46 (e) 150 and 225 (f) 96 and 128 U Exercise 9 Answer the following questions: E 1. List all the factors for each of the following numbers: (a) 70 (b) 95 (c) 224 N (d) 250 (e) 729 LI 2. Write the prime factors for each of the following numbers: (a) 108 (b) 120 N (c) 840 O 3. Write the common factors of each of the following pairs of numbers (a) 9 and 15 (b) 12 and 72 R (c) 8 and 32 FO 4. Find the common factors of each of the following pairs of numbers. (a) 60 and 200 (b) 28 and 32 114 MATH std 5.indd 114 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 5. List the first 8 multiples for each of the following numbers: (a) 7 (b) 9 (c) 13 (d) 20 (e) 34 6. Find the LCM of 24 and 27 by using prime factors. 7. List all prime numbers between 30 and 40. LY 8. Write the type of a number which results from adding: (a) Two even numbers N (b) An odd number and an even number (c) Two odd numbers O 9. Find the GCF of each of the following pairs of numbers: (a) 8 and 12 (d) 15 and 30 (b) 6 and 18 SE (c) 14 and 28 U 10. Find the LCM of each of the following pairs of numbers: (a) 2 and 3 (b) 4 and 6 (c) 7 and 4 (d) 5 and 7 E N 11. Draw a chart of numbers from 1 to 100 and use it to answer the following questions: LI (a) Write the first five multiples for each of the following numbers: (i) 11 N (ii) 29 O (iii) 33 (b) Write all even numbers between 70 and 83. (c) Write all prime numbers between 50 and 99. R (d) List all odd numbers between 85 and 100. FO 115 MATH std 5.indd 115 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Summary 1. A prime number is a number with only two factors, which are 1 and the number itself. 2. Factors are numbers which divide a given number without a remainder. 3. Multiples are numbers which are divisible by the given number without a remainder. 4. 2 is the only number which is both even and prime. LY 5. Even numbers are numbers that are divisible by 2. 6. Odd numbers are numbers that are not divisible by 2. N O SE U E N LI N O R FO 116 MATH std 5.indd 116 30/07/2021 14:49