Learning objectives

• Use divisibility rules for 2, 3, 4, 5, 6, 9 and 10.
• Decide quickly whether a number divides another.

Key ideas

A number is divisible by 2 if its last digit is even; by 3 if the sum of its digits is divisible by 3; by 4 if its last two digits form a number divisible by 4; by 5 if it ends in 0 or 5; by 6 if it is divisible by both 2 and 3; by 9 if the sum of its digits is divisible by 9; and by 10 if it ends in 0.

Worked example

Is 4,725 divisible by 9? 4 + 7 + 2 + 5 = 18, and 18 is divisible by 9, so yes.

Practice

1. Is 3,462 divisible by 6?
2. Is 7,128 divisible by 4?
3. Find a 3-digit number divisible by both 5 and 9.

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