How to tell if a number is divisible by 12
12 is 2 × 6 and also 3 × 4, but only one of those pairs gives a working test.
A number is divisible by 12 when it divides by 3 and by 4.
How to check it
- Add the digits. If the total is a multiple of 3, the first half passes.
- Look at the last two digits. If they make a multiple of 4, the second half passes.
- Both have to pass for the number to divide by 12.
Worked examples
Is 4620 divisible by 12?
4 + 6 + 2 + 0 = 12 → multiple of 3 ✓ last two digits 20 = 4 × 5 ✓
Both pass, so yes. 4620 = 12 × 385.
Is 42 816 divisible by 12?
4 + 2 + 8 + 1 + 6 = 21 → multiple of 3 ✓ last two digits 16 = 4 × 4 ✓
Yes. 42 816 = 12 × 3568.
Is 4626 divisible by 12?
4 + 6 + 2 + 6 = 18 → multiple of 3 ✓ last two digits 26 → not a multiple of 4 ✗
No. It divides by 6, but not by 12.
Why 3 and 4, and not 2 and 6
A pair of tests only proves divisibility by their product when the two numbers share no divisor apart from 1, which is what coprime means. 3 and 4 share nothing but 1, so passing both means the number holds a 3 and two factors of 2, which is a 12.
2 and 6 overlap: 6 already contains a 2, so passing both only proves the number contains a 6 and at least one 2, which it already had. 18 divides by 2 and by 6 and does not divide by 12.
Where mistakes happen
- Testing 2 and 6. It is the most natural split of 12 and it lets numbers like 18, 30 and 42 through.
- Testing 4 and stopping because the number is obviously even.
- Using the 6 test and assuming 12 follows. Every multiple of 12 divides by 6, but not the other way round.
Questions people ask
Is there a single-step rule for 12?
No. Two rules you already know are faster than a new one you would have to learn.