Division Tricks
Divisibility by 2 – Just Look at the Last Digit
Is a number even? You never need to divide: one glance at the last digit tells you.
This page explains the rule, shows why it works, and walks through worked examples. Then you can try it yourself and check your understanding with practice questions. Use the previous and next links at the bottom to move through the tricks in order.
The rule
The Rule: If a number ends in an even digit - 0, 2, 4, 6, or 8 - it is divisible by 2.
Why it works
Why It Works: Think of any number as a stack of place-value chunks: hundreds, tens, and ones. Every chunk except the very last one is a multiple of 10 (like 10, 20, 100, 240 …), and multiples of 10 are always even. So the only chunk that can possibly make the whole number odd is the ones digit — the single digit you see at the very end. That is why checking just that one digit is always enough.
Formal Proof (for advanced learners)
Let N be any whole number, and write it as N = 10a + b, where b is N’s units digit (0–9) and a is the number formed by all the remaining digits. Since 10a is always even for any whole number a, N is even exactly when b is even. In modular notation, N ≡ b (mod 2), so checking whether b ∈ {0, 2, 4, 6, 8} fully decides divisibility by 2.
Examples
- 28 ends in 8, so it’s divisible by 2.
- 46 ends in 6, so it’s divisible by 2.
- 133 ends in 3, so it is not divisible by 2.
Step by step
Example A: is 5678 divisible by 2?
- The last digit of 5678 is 8.
- 8 is even (the even digits are 0, 2, 4, 6 and 8).
- So 5678 is divisible by 2.
Example B: is 90137 divisible by 2?
- The last digit of 90137 is 7.
- 7 is odd (the even digits are 0, 2, 4, 6 and 8).
- So 90137 is not divisible by 2.
Try it yourself
Now it is your turn. A new random question appears each time. Choose True or False. If you are right, we show how the trick got you there, step by step. If you are not, you will see the full working two ways, the shortcut and the usual method, so you can spot exactly where your answer differed. Press New Question as often as you like: a few quick rounds is the best way to make the trick feel automatic.
Practice questions
Have a go on paper first, then tap Show answer to check your method.
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Is 74 divisible by 2?
Show answer
Yes. The last digit of 74 is 4. 4 is even (the even digits are 0, 2, 4, 6 and 8). So 74 is divisible by 2.
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Is 391 divisible by 2?
Show answer
No. The last digit of 391 is 1. 1 is odd (the even digits are 0, 2, 4, 6 and 8). So 391 is not divisible by 2.
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Is 1250 divisible by 2?
Show answer
Yes. The last digit of 1250 is 0. 0 is even (the even digits are 0, 2, 4, 6 and 8). So 1250 is divisible by 2.
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Is 8003 divisible by 2?
Show answer
No. The last digit of 8003 is 3. 3 is odd (the even digits are 0, 2, 4, 6 and 8). So 8003 is not divisible by 2.
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Can 46218 stickers be shared equally among 2 friends with none left over?
Show answer
Yes. The last digit of 46218 is 8. 8 is even (the even digits are 0, 2, 4, 6 and 8). So 46218 is divisible by 2.
Tips and watch-outs
- Zero counts as even, so 130 and 4000 are both divisible by 2.
- Only the last digit matters. 2461 is odd because it ends in 1, however many even digits come before it.