How to tell if a number is divisible by 2
This is the first divisibility rule most children meet, and the one that makes all the others believable: you can answer it for a four-digit number faster than you can pick up a pencil.
A number is divisible by 2 when its last digit is 0, 2, 4, 6 or 8. Those are exactly the even numbers.
How to check it
- Ignore every digit except the last one.
- Look at that last digit on its own.
- If it is 0, 2, 4, 6 or 8, the number divides by 2. If it is 1, 3, 5, 7 or 9, it does not.
Worked examples
Is 4620 divisible by 2?
4620 ends in 0
Yes. 4620 = 2 × 2310.
Is 1155 divisible by 2?
1155 ends in 5
No. 1155 is odd.
Is 39 874 divisible by 2?
39 874 ends in 4
Yes. The size of the number makes no difference at all.
Why only the last digit matters
Count in 2s and watch the last digit: 2, 4, 6, 8, 0, and then the same five over again. A multiple of 2 can never end in anything else.
Every ten splits evenly into 2s: ten is five 2s, a hundred is fifty 2s, a thousand is five hundred 2s. So every part of the number above the units column has already been shared out perfectly, no matter how big it is.
That leaves only the last digit to decide the question. 4620 is 462 tens, all of them even splits, plus 0 left over. The 0 is the only part that can spoil it.
Where it goes wrong
- Adding the digits up first. That is the rule for 3 and 9; for 2 you only ever look at the end.
- Assuming a long number is harder. 8 675 309 takes exactly as long as 9 does.
- Thinking a number that ends in 0 might be odd. Anything ending in 0 divides by 2, by 5 and by 10.
Questions people ask
Is 0 divisible by 2?
Yes. 0 ÷ 2 = 0 with nothing left over, so 0 is an even number.
What about negative numbers?
The same rule works: −38 ends in 8, so it divides by 2. The minus sign changes nothing.
Is every number that ends in an even digit divisible by 2?
Yes, and there are no exceptions. That is what makes this rule the easiest of the set.