Grade 5 · Unit 1: Number and place value

Divisibility rules

Know without dividing.

Packing evenly

Can 1236 pens be packed equally in boxes of 4? A divisibility rule answers quickly. No long division needed!

Rules for 2, 4, 5, 10

1236: last two digits 36, and 36 ÷ 4 = 9. So 1236 is divisible by 4. The pens fit exactly in boxes of 4.

Rules for 3, 6, 9

4572: digit sum = 4 + 5 + 7 + 2 = 18. 18 is divisible by 3 and by 9. 4572 is even too, so it is divisible by 6.

Why it works

10, 100 and 1000 are each 1 more than a multiple of 9. So dividing by 9 leaves the digit sum. That is why the digit-sum rule works for 3 and 9.

Why odd and even?

An even number can be split into 2 equal rows; an odd number leaves 1 over. Every even number is 2 × something; every odd number is 2 × something + 1. So even + even = even, odd + odd = even and odd + even = odd.

What I learnt

• I can use divisibility rules.
• I can explain why some rules work.