Divisibility Rules — Quick Checks (Grades 4–5)
Divisibility rules let you tell whether one number divides another without doing the full division.
Understanding divisibility rules
A number is divisible by 2 if it's even (ends in 0,2,4,6,8); by 5 if it ends in 0 or 5; by 10 if it ends in 0; by 3 if the sum of its digits is divisible by 3; by 9 if the digit sum is divisible by 9. These shortcuts make factoring and simplifying much faster.
Key Idea
Why do they work? Every ten is already a multiple of 2, 5 and 10, so for those three only the last digit decides. For 3 and 9, use 10 = 9 + 1 and 100 = 99 + 1: 126 is 1 hundred, 2 tens and 6 ones, which is (1 × 99 + 2 × 9) + (1 + 2 + 6). The first part is always a multiple of 9, and so of 3, so whether the whole number divides by 3 or 9 comes down to the digit sum.
Seeing it in action
Worked example
Is 126 divisible by 3?
Add the digits: 1 + 2 + 6 = 9. 9 is divisible by 3. → Yes (126 = 3 × 42).
Digit sum 9 shows 126 is divisible by 3.
Worked example 2: a no
Is 124 divisible by 3?
Add the digits: 1 + 2 + 4 = 7. 7 is not divisible by 3. → No (124 = 3 × 41 + 1, so there is 1 left over).
A common mistake, and the fix
Using the digit-sum test for the wrong divisor.
The digit-sum test works for 3 and 9, not for 4: 124 has a digit sum of 7, yet 124 = 4 × 31. For 6, a number must pass both the test for 2 and the test for 3.
Try a few
Is 75 divisible by 2?
it ends in 5, so it's odd.
Is 45 divisible by 9?
4 + 5 = 9.
Is 214 divisible by 3?
2 + 1 + 4 = 7, and 7 isn't divisible by 3.
Try it in Numeris.
A short lesson, then practice with feedback on every answer.
Put the reasoning on paper.
Try six fraction, angle, perimeter and area questions with explained answers, for grades 4–6.
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