Divisibility by 5

A number is divisible by 5 if its last digit is 0 or 5.

Examples

A number that ends in 0 is divisible by 2, by 5 and by 10. For example, 1,760 = 176 × 10.

Split the number into tens and ones: 425 = 420 + 5.
420 is 42 tens, and 10 = 5 × 2, so 420 is divisible by 5. Only the last digit is left to check:

425 = 420 ✓ + 5 ✓ → divisible by 5
428 = 420 ✓ + 8 ✗ → not divisible by 5

This uses the rule for the divisibility of a sum.

Careful: ending in 5 does not mean divisible by 25. 35 ends in 5, but 35 ÷ 25 = 1 R 10. See divisibility by 25.

5 is half of 10, so you can work with 10 and 2 instead.

Task	Trick	Examples
Divide by 5	Multiply by 2, then divide by 10	415 ÷ 5: 415 × 2 = 830, 830 ÷ 10 = 83 342 ÷ 5: 342 × 2 = 684, 684 ÷ 10 = 68.4
Multiply by 5	Divide by 2, then multiply by 10	62 × 5: 62 ÷ 2 = 31, 31 × 10 = 310 47 × 5: 47 ÷ 2 = 23.5, 23.5 × 10 = 235
Square a two-digit number ending in 5	Multiply the tens digit by the next number, then write 25 after the result	35²: 3 × 4 = 12 → 1,225 85²: 8 × 9 = 72 → 7,225

Click a question to see the answer.

1. Which of these numbers are divisible by 5: 135, 552, 2,000, 7,005, 9,999?

135, 2,000 and 7,005 – they end in 5, 0 and 5.

2. Which digits can go in the box so that 47 is divisible by 5?

0 or 5: 470 and 475.

3. Divide quickly: 235 ÷ 5

235 × 2 = 470, 470 ÷ 10 = 47

4. Multiply quickly: 86 × 5

86 ÷ 2 = 43, 43 × 10 = 430

5. Square quickly: 45²

4 × 5 = 20, then write 25 after it: 2,025

6. A number is divisible by both 2 and 5. What must its last digit be?

0. For 2 the last digit must be 0, 2, 4, 6 or 8; for 5 it must be 0 or 5. Only 0 is on both lists.