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F.1 Review divisibility rules

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What are divisibility rules?

Divisibility rules are quick ways to decide if one number can be divided evenly by another number—without doing long division. They help you find factors, simplify fractions, and recognize number patterns.

Example:
  • 24 is divisible by 3 because 2 + 4 = 6, and 6 is divisible by 3.
  • 50 is divisible by 5 because it ends in 0.
Note

If a number divides evenly (with no remainder), it is said to be “divisible” by that number.

Divisibility rule for 2

A number is divisible by 2 if it is an even number.

How to identify:
  • Look at the last digit of the number.
  • If the last digit is 0, 2, 4, 6, or 8, the number is divisible by 2.
Example:
  • 248 ends with 8, so it is divisible by 2.
Note

All even numbers are divisible by 2.

Divisibility rule for 3

A number is divisible by 3 if the sum of its digits is divisible by 3.

How to identify:
  • Add all the digits in the number.
  • If the total is divisible by 3, then the whole number is divisible by 3.
Example:
  • For 123 → 1 + 2 + 3 = 6. Since 6 is divisible by 3, 123 is divisible by 3.
Note

This rule works for any size number—just keep adding the digits until you can tell if it’s divisible by 3.

Divisibility rule for 4

A number is divisible by 4 if the number formed by its last two digits is divisible by 4.

How to identify:
  • Look at the last two digits of the number.
  • If those two digits form a number divisible by 4, the entire number is divisible by 4.
Example:
  • In 3,216, the last two digits form 16. Since 16 ÷ 4 = 4, 3,216 is divisible by 4.
Note

All numbers ending in 00, 04, 08, 12, 16, 20, and so on are divisible by 4.

Divisibility rule for 5

A number is divisible by 5 if its last digit is 0 or 5.

How to identify:
  • Check the last digit of the number.
  • If it is 0 or 5, the number is divisible by 5.
Example:
  • 85 ends with 5, so it is divisible by 5.
Note

Every number that ends in 0 or 5 has 5 as a factor.

Divisibility rule for 6

A number is divisible by 6 if it is divisible by both 2 and 3.

How to identify:
  • Check that the number is even (divisible by 2).
  • Then check if the sum of its digits is divisible by 3.
Example:
  • For 132: it’s even, and 1 + 3 + 2 = 6 (divisible by 3), so 132 is divisible by 6.
Note

This rule combines two smaller rules—if both conditions are true, the number is divisible by 6.

Divisibility rule for 8

A number is divisible by 8 if the last three digits of the number form a number that is divisible by 8.

How to identify:
  • Look at the last three digits of the number.
  • If those three digits form a number divisible by 8, then the whole number is divisible by 8.
Example:
  • For 6,416 → the last three digits are 416. Since 416 ÷ 8 = 52, 6,416 is divisible by 8.
Note

For smaller numbers (less than 1,000), you can directly check if the number itself is divisible by 8.

Divisibility rule for 9

A number is divisible by 9 if the sum of its digits is divisible by 9.

How to identify:
  • Add all the digits in the number.
  • If the total is divisible by 9, then the number is divisible by 9.
Example:
  • For 729 → 7 + 2 + 9 = 18. Since 18 is divisible by 9, 729 is divisible by 9.
Note

The divisibility rules for 3 and 9 are similar—9’s rule is just a stronger version of 3’s rule.

Divisibility rule for 10

A number is divisible by 10 if it ends in 0.

How to identify:
  • Look at the last digit of the number.
  • If it is 0, the number is divisible by 10.
Example:
  • 340 ends with 0, so it is divisible by 10.
Note

Every multiple of 10 ends in zero. This rule is the easiest one to remember!

Using divisibility rules in problem solving

Divisibility rules make it easier to find factors, simplify fractions, and check if numbers are prime or composite without dividing.

Examples:
  • To check if 84 is divisible by 6: it’s even (divisible by 2) and 8 + 4 = 12 (divisible by 3), so 84 is divisible by 6.
  • To simplify 90/150: both end in 0 (divisible by 10), so 90 ÷ 10 = 9 and 150 ÷ 10 = 15 → 9/15 simplifies further to 3/5.
Note

Mastering these rules will help you solve math problems faster and with greater confidence.