Division Tricks
Divisibility by 4 – Check the Last Two Digits
However long the number is, divisibility by 4 depends only on its last two digits.
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 the last two digits of a number form a number divisible by 4, then the entire number is divisible by 4.
Why it works
Why It Works: Any number can be split into “full hundreds” plus “whatever is left in the last two digits.” A hundred happens to be 4 × 25, so every full hundred is already a clean multiple of 4 and never affects the test. That leaves only the number formed by the last two digits to actually check.
Formal Proof (for advanced learners)
Write N = 100a + b, where b is the two-digit number (0–99) formed by N’s last two digits and a is everything before that. Since 100 = 4·25, we have 100a ≡ 0 (mod 4), so N ≡ b (mod 4). Hence N is divisible by 4 exactly when its last two digits, read as a number, are divisible by 4.
Examples
- 132 → last two digits 32, divisible by 4.
- 3116 → last two digits 16, divisible by 4.
- 750 → last two digits 50, not divisible by 4.
Step by step
Example A: is 3712 divisible by 4?
- Look at the last two digits of 3712: they make 12.
- 12 ÷ 4 = 3.
- So 3712 is divisible by 4.
Example B: is 9506 divisible by 4?
- Look at the last two digits of 9506: they make 6.
- 6 ÷ 4 = 1 remainder 2, so 4 does not go in exactly.
- So 9506 is not divisible by 4.
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 48 divisible by 4?
Show answer
Yes. Look at the last two digits of 48: they make 48. 48 ÷ 4 = 12. So 48 is divisible by 4.
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Is 90 divisible by 4?
Show answer
No. Look at the last two digits of 90: they make 90. 90 ÷ 4 = 22 remainder 2, so 4 does not go in exactly. So 90 is not divisible by 4.
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Is 316 divisible by 4?
Show answer
Yes. Look at the last two digits of 316: they make 16. 16 ÷ 4 = 4. So 316 is divisible by 4.
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Is 1528 divisible by 4?
Show answer
Yes. Look at the last two digits of 1528: they make 28. 28 ÷ 4 = 7. So 1528 is divisible by 4.
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Can 72350 pencils be packed into boxes of 4 with none left over?
Show answer
No. Look at the last two digits of 72350: they make 50. 50 ÷ 4 = 12 remainder 2, so 4 does not go in exactly. So 72350 is not divisible by 4.
Tips and watch-outs
- Read the last two digits as one number. In 1308 look at 08, which is just 8, and 8 is divisible by 4.
- Any number ending in 00 is divisible by 4, because 100 = 4 × 25.