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Division practice

Divisibility rules

Use a printable reference for divisibility by 2, 3, 4, 5, 6 and 9, then explain why a number passes a particular test.

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Read the rule for the divisor you are testing. Check the required digits or digit sum, then explain whether the original number divides evenly.

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Learning objective

What this activity builds

Choose a useful divisibility rule and apply it without carrying out the full division.

Worked example

Is 324 divisible by both 4 and 9?

Yes: 324 ÷ 4 = 81 and 324 ÷ 9 = 36.

Its last two digits, 24, form a multiple of 4. Its digit sum is 3 + 2 + 4 = 9, a multiple of 9. Each test gives a separate reason that the division is exact.

Teaching notes

Make the practice count

  • Compare the tests for 3 and 9 using numbers that pass only the test for 3.
  • Ask the learner to name the digits used by a rule before applying it.

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Math SheetNameScoreTeacherDateDivisibility RulesUse the rules for 2, 3, 4, 5, 6, and 9 as a reference.1.Divisible by 2The ones digit is even: 0, 2, 4, 6, or 8.Divisible by 3The sum of the digits is divisible by 3.Divisible by 4The last two digits form a multiple of 4.Equivalently, ones + twice the tens is divisible by 4.If tens is even, ones is 0, 4, or 8; if tens is odd, ones is 2 or 6.Divisible by 5The ones digit is 0 or 5.Divisible by 6The number is divisible by both 2 and 3.Divisible by 9The sum of the digits is divisible by 9.math-sheet.comPage 1 / 1

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