Divisibility tests
Objective. Apply tests for divisibility by 2, 3, 4, 5, 9 and 10.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
A divisibility test is a quick check that tells you whether one number divides exactly into another, without doing the full division. For example, a number is divisible by 2 if its last digit is even, and divisible by 5 if it ends in 0 or 5. A number is divisible by 3 if the sum of its digits is divisible by 3, so 471 works because 4+7+1=12. Divisibility by 9 uses the same digit-sum idea but checks for a multiple of 9. Divisibility by 4 depends only on the last two digits forming a multiple of 4, such as 316 because 16÷4=4.
Worked example
Using divisibility tests, determine whether 846 is divisible by 2, 3 and 9.
- 1Check the last digit: 846 ends in 6, which is even, so it is divisible by 2.
- 2Sum the digits: 8+4+6=18.
- 3Since 18 is divisible by 3, 846 is divisible by 3; since 18 is divisible by 9, 846 is divisible by 9.
- 4Confirm by division: 846÷9=94 exactly.
Answer: 846 is divisible by 2, 3 and 9
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Practice
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Start practisingCommon mistake. Pupils sometimes apply the digit-sum rule to test for 4 or divide by the wrong digit for the test, such as checking only the first digit for divisibility by 2. Always check the correct digits named in each rule.
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