6 Questions
What is the rule for checking the divisibility of a number by 3?
If the sum of its digits is divisible by 3
Which of the following numbers is divisible by 9?
945
What is the condition for a number to be divisible by 6?
If the number is divisible by both 2 and 3
What are the prime factors of the number 15?
3 and 5
What is the remainder when 23 is divided by 7?
1
Why is the remainder always less than the divisor?
Because the remainder is defined as the amount left over
Study Notes
Divisibility Rules
Divisibility By 3
- A number is divisible by 3 if the sum of its digits is divisible by 3.
- Example: 123 is divisible by 3 because 1 + 2 + 3 = 6, which is divisible by 3.
Divisibility By 9
- A number is divisible by 9 if the sum of its digits is divisible by 9.
- Example: 459 is divisible by 9 because 4 + 5 + 9 = 18, which is divisible by 9.
Divisibility By 6
- A number is divisible by 6 if it is divisible by both 2 and 3.
- A number is divisible by 2 if it ends in 0, 2, 4, 6, or 8.
- Combine the rules for divisibility by 2 and 3 to check for divisibility by 6.
- Example: 120 is divisible by 6 because it ends in 0 (divisible by 2) and 1 + 2 + 0 = 3, which is divisible by 3.
Prime Factors
- A prime factor is a prime number that divides a given number exactly without leaving a remainder.
- Every composite number can be expressed as a product of prime factors in a unique way.
- Example: The prime factors of 12 are 2, 2, and 3 because 2 × 2 × 3 = 12.
Remainders
- A remainder is the amount left over when one number is divided by another.
- When dividing a number by a divisor, the remainder is always less than the divisor.
- Example: When dividing 17 by 5, the quotient is 3 and the remainder is 2 because 17 = 3 × 5 + 2.
Divisibility Rules
Divisibility By 3
- A number is divisible by 3 if the sum of its digits is divisible by 3.
- The sum of digits is calculated by adding up individual digits of the number.
- Example: 123 is divisible by 3 because 1 + 2 + 3 = 6, which is divisible by 3.
Divisibility By 9
- A number is divisible by 9 if the sum of its digits is divisible by 9.
- The sum of digits is used to determine divisibility by 9.
- Example: 459 is divisible by 9 because 4 + 5 + 9 = 18, which is divisible by 9.
Divisibility By 6
- A number is divisible by 6 if it is divisible by both 2 and 3.
- A number is divisible by 2 if it ends in 0, 2, 4, 6, or 8.
- Combine the rules for divisibility by 2 and 3 to check for divisibility by 6.
- Example: 120 is divisible by 6 because it ends in 0 (divisible by 2) and 1 + 2 + 0 = 3, which is divisible by 3.
Prime Factors
- A prime factor is a prime number that divides a given number exactly without leaving a remainder.
- Every composite number can be expressed as a product of prime factors in a unique way.
- Example: The prime factors of 12 are 2, 2, and 3 because 2 × 2 × 3 = 12.
Remainders
- A remainder is the amount left over when one number is divided by another.
- The remainder is always less than the divisor.
- Example: When dividing 17 by 5, the quotient is 3 and the remainder is 2 because 17 = 3 × 5 + 2.
Learn the rules to determine if a number is divisible by 3, 6, or 9. Understand the simple methods to check for divisibility.
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