Division
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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Divisibility tests
Test whole numbers against the fixed set of divisors 2, 3, 4, 5, 6 and 9, recording every rule that the number satisfies.
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Check each listed divisor independently. A number can pass several tests, and a number that fails this set is not necessarily prime.
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What this activity builds
Apply several divisibility tests to the same number and distinguish a failed test from a prime-number claim.
Worked example
Which of 2, 3, 4, 5, 6 and 9 divide 438 evenly?
2, 3 and 6.
438 is even and its digit sum, 15, is divisible by 3, so it also passes the test for 6. The last two digits, 38, fail the test for 4; the final digit fails the test for 5; and 15 is not divisible by 9.
Teaching notes
Make the practice count
- Record evidence for each yes or no instead of stopping at the first divisor.
- Use 49 to show that failing this particular set of tests does not establish that a number is prime.
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Related activities
Division
Divisibility with chosen divisors
Focus divisibility practice on selected divisors from 2 through 12 and determine which of them divide each whole number exactly.
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