How to tell if a number is divisible by 10
The rule
A whole number is divisible by 10 if its final digit is 0.
How to check it
- Look at the last digit.
- If it is 0, the number divides by 10.
Worked examples
Is 4620 divisible by 10?
4620 ends in 0
Yes. 4620 = 10 × 462.
Is 1155 divisible by 10?
1155 ends in 5
No. It divides by 5 but not by 10.
Is 900 000 divisible by 10?
ends in 0
Yes, and by 100, and by 1000, for the same reason.
Why the last digit is the whole answer
Count in 10s and watch the last digit: it is 0 every time, however far you go. A multiple of 10 can never end in anything else.
The reason is in how we write numbers: 4620 means 462 tens and 0 units, and those 462 tens are already a whole number of 10s.
So the only thing that can be left over is the units digit, and the only units digit that is itself a whole number of 10s is 0.
The same argument explains the remainder: whatever the last digit is, that is exactly what is left after dividing by 10.
Where mistakes happen
- Confusing it with the rule for 5. Ending in 5 passes for 5 and fails for 10.
- Thinking a number needs a 0 somewhere in it. 105 contains a 0 and does not divide by 10; only the final position counts.
Questions people ask
Does a multiple of 10 always divide by 2 and 5?
Yes. 10 = 2 × 5, so anything ending in 0 passes all three tests.
How do I check for 100?
The same idea one place along: it has to end in two zeros. For 1000, three.
Is 0 divisible by 10?
Yes. 0 ÷ 10 = 0 with nothing left over, because 10 × 0 = 0. 0 is divisible by every whole number from 1 up.
Is 10 divisible by 0?
No. Nothing can be divided by 0. 10 ÷ 0 would need a number that makes 10 when you multiply it by 0, and any number multiplied by 0 is 0.
Which numbers are not divisible by 10?
Every whole number whose final digit is not 0, such as 15, 104 and 999. A number ending in 5 divides by 5, but not by 10.
What is 10 divisible by?
1, 2, 5 and 10. Those are the factors of 10, and they are the only whole numbers that go into it exactly.