Math Gr 8 Ch 1: Multiples and Factors
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Questions and Answers

What is a multiple of a number?

  • The product of that number and a fraction.
  • The difference of that number and an integer.
  • The sum of that number and an integer.
  • The product of that number and an integer. (correct)

What are the factors of 20?

  • 1, 3, 5, 10
  • 2, 4, 6, 8, 10
  • 1, 2, 4, 5, 10, 20 (correct)
  • 1, 5, 10, 20

What is a characteristic of prime numbers?

  • They can be formed by multiplying two smaller natural numbers.
  • They are always even numbers.
  • They have exactly two distinct positive divisors: 1 and itself. (correct)
  • They have more than two factors.

What is prime factorization?

<p>The process of expressing a number as the product of its prime factors. (C)</p> Signup and view all the answers

What is the least common multiple (LCM) of two or more numbers?

<p>The smallest multiple that two or more numbers have in common. (C)</p> Signup and view all the answers

How do you find the highest common factor (HCF) of two or more numbers?

<p>Take the lowest power of each prime factor that appears in the factorization of each number. (C)</p> Signup and view all the answers

What is a characteristic of composite numbers?

<p>They have more than two factors. (C)</p> Signup and view all the answers

What is the key concept of prime factorization?

<p>Every composite number can be expressed as a product of prime factors. (C)</p> Signup and view all the answers

Which of the following is a characteristic of multiples of a number?

<p>They form a sequence where each term is that number multiplied by an integer (D)</p> Signup and view all the answers

What is the relationship between factors of a number?

<p>They come in pairs, and each pair multiplies to give the original number (A)</p> Signup and view all the answers

Which of the following is true about prime numbers?

<p>They can only be divided by 1 and themselves (D)</p> Signup and view all the answers

What is the process of expressing a number as the product of its prime factors called?

<p>Prime factorization (A)</p> Signup and view all the answers

How do you find the LCM of two or more numbers?

<p>Take the highest power of each prime factor that appears in the factorization of each number (D)</p> Signup and view all the answers

What is the difference between the LCM and HCF of two or more numbers?

<p>LCM is the largest multiple, while HCF is the smallest factor (B)</p> Signup and view all the answers

Which of the following is a characteristic of composite numbers?

<p>They have more than two distinct positive divisors (B)</p> Signup and view all the answers

What is the key concept of prime factorization?

<p>Every number can be expressed as a product of prime factors, and this representation is unique, apart from the order of the factors (B)</p> Signup and view all the answers

What is the result of dividing a number by its highest common factor?

<p>The quotient is always 1 (A)</p> Signup and view all the answers

What is the purpose of finding the prime factors of a number?

<p>To express the number as a product of prime factors (B)</p> Signup and view all the answers

Which of the following statements is true about the factors of a composite number?

<p>The factors come in pairs (A)</p> Signup and view all the answers

What is the relationship between the prime factors of a number and its multiples?

<p>The prime factors are the building blocks of the multiples (B)</p> Signup and view all the answers

What is the result of finding the least common multiple of two or more numbers?

<p>The smallest multiple that the numbers have in common (D)</p> Signup and view all the answers

What is the difference between a prime number and a composite number?

<p>A prime number has only two factors, while a composite number has more than two factors (B)</p> Signup and view all the answers

What is the purpose of finding the highest common factor of two or more numbers?

<p>To find the largest number that divides the numbers without leaving a remainder (B)</p> Signup and view all the answers

Which of the following statements is true about the number of factors of a prime number?

<p>A prime number has exactly two factors (A)</p> Signup and view all the answers

Which of the following statements is true about the multiples of a number?

<p>They can be both prime and composite numbers. (C)</p> Signup and view all the answers

What is the relationship between the prime factors of a number and its factors?

<p>The prime factors are a subset of the factors. (D)</p> Signup and view all the answers

What is the purpose of finding the prime factors of a number?

<p>To express the number as a product of prime numbers. (D)</p> Signup and view all the answers

Which of the following statements is true about the HCF of two or more numbers?

<p>It is always a factor of the numbers. (A)</p> Signup and view all the answers

What is the relationship between the LCM and HCF of two or more numbers?

<p>The LCM is always greater than the HCF. (D)</p> Signup and view all the answers

Which of the following statements is true about the factors of a composite number?

<p>They can be both prime and composite numbers. (D)</p> Signup and view all the answers

What is the result of dividing a number by its HCF?

<p>The result is always a factor of the number. (A)</p> Signup and view all the answers

Which of the following statements is true about the prime factors of a number?

<p>They are always unique. (D)</p> Signup and view all the answers

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