Divisibility by 25

A number is divisible by 25 if it ends in 00, 25, 50 or 75.

Easy to remember with quarters: 25¢, 50¢, 75¢, $1.00.

Examples

Why it works

100 = 25 × 4, so any number of hundreds is divisible by 25. Split off the hundreds, and only the last two digits are left to check:

8,375 = 8,300 ✓ + 75 ✓ → divisible by 25
8,345 = 8,300 ✓ + 45 ✗ → not divisible by 25

From 00 to 99, only 00, 25, 50 and 75 are divisible by 25 – that's where the rule comes from. It uses the rule for the divisibility of a sum. Divisibility by 4 also uses the last two digits, for the same reason: 100 = 4 × 25.

Careful: every number divisible by 25 is also divisible by 5, but not the other way around. 35, 110 and 2,045 end in 5 or 0, but they end in 35, 10 and 45, so they are not divisible by 25. See divisibility by 5.

Try it yourself

Click a question to see the answer.

1. Which of these numbers are divisible by 25: 650, 1,205, 3,475, 10,010, 9,900?

650, 3,475 and 9,900 – they end in 50, 75 and 00.

2. Which digits can go in the box so that 6,45 is divisible by 25?

The number must end in 25 or 75, so the answer is 2 or 7: 6,425 and 6,475.

3. Which digits can go in the box so that 3,10 is divisible by 25?

The number must end in 00 or 50, so the answer is 0 or 5: 3,100 and 3,150.

4. How many whole numbers from 1 to 200 are divisible by 25?

25, 50, 75, 100, 125, 150, 175, 200 – 8 numbers.

5. How many quarters make $3.75?

$3.75 = 375¢ and 375 ÷ 25 = 15. 15 quarters

6. A number is divisible by both 4 and 25. What are its last two digits?

00. The ending must be 00, 25, 50 or 75, and of these only 00 is divisible by 4. So the number is divisible by 100.