How to tell if a number is divisible by 5
Counting in fives (5, 10, 15, 20, 25), the ending goes 5, 0, 5, 0 and never anything else. That pattern never breaks, however far you count, and it is the whole rule.
A number is divisible by 5 when its last digit is 0 or 5.
How to check it
- Look at the last digit and nothing else.
- If it is 0 or 5, the number divides by 5.
- Any other last digit means it does not.
Worked examples
Is 1155 divisible by 5?
1155 ends in 5
Yes. 1155 = 5 × 231.
Is 4620 divisible by 5?
4620 ends in 0
Yes. 4620 = 5 × 924.
Is 1147 divisible by 5?
1147 ends in 7
No. 7 is not 0 or 5. 1147 = 5 × 229 with 2 left over.
Why the ending settles it
Every ten is exactly two 5s, so every ten, hundred and thousand in the number has already been shared into 5s with nothing left over.
The only part that has not been shared out is the last digit, and of the ten digits only 0 and 5 are themselves whole numbers of 5s.
Where it goes wrong
- Assuming a number ending in 0 divides only by 10. It divides by 10, and also by 5 and by 2.
- Looking for a digit 5 anywhere in the number. 5 213 contains a 5 and does not divide by 5; only the last position counts.
Questions people ask
Is every multiple of 10 also a multiple of 5?
Yes, because 10 is 2 × 5. Anything ending in 0 passes both tests.
Can an odd number divide by 5?
Certainly. 15, 25 and 1155 are all odd multiples of 5. Ending in 5 means odd, ending in 0 means even.