How to tell if a number is divisible by 4
Being even is not enough for 4: 18 and 30 are both even and neither divides by 4.
A number is divisible by 4 when the number made by its last two digits is a multiple of 4.
How to check it
- Cover everything except the last two digits.
- Ask whether those two digits, read as a number, are a multiple of 4.
- If they are, the whole number divides by 4. A number ending in 00 always does.
Worked examples
Is 4620 divisible by 4?
last two digits: 20 → 20 = 4 × 5
Yes. 4620 = 4 × 1155.
Is 1918 divisible by 4?
last two digits: 18 → 16 and 20 are multiples of 4, 18 is not
No, even though 1918 is even.
Is 7 300 divisible by 4?
last two digits: 00
Yes. Every hundred is a whole number of 4s, so anything ending in 00 divides by 4.
The other way: halve it twice
Because 4 = 2 × 2, a number divides by 4 exactly when you can halve it twice and still have a whole number. 4620 → 2310 → 1155: both halvings landed, so it divides by 4.
Try it on 1918: 1918 → 959, and 959 is odd, so halving again gives 479.5 rather than a whole number. 1918 does not divide by 4.
Halving is often quicker on numbers whose last two digits are awkward.
Why the last two digits are enough
Every hundred is 4 × 25, so hundreds, thousands and everything above them are already whole numbers of 4s. They can never be the reason a number fails the test.
That leaves the last two digits holding the entire answer. 4620 is 46 hundreds, all clean, plus 20, and only that 20 can decide it.
Where mistakes happen
- Checking only the last digit. 18, 30 and 42 are all even and none divides by 4.
- Halving only once. One halving tests 2, not 4. It has to land twice.
- Forgetting that 00 counts. 500 and 1900 both pass, because 0 is a multiple of 4.
Questions people ask
Is every multiple of 4 also a multiple of 2?
Yes. 4 contains a 2, so anything that divides by 4 automatically divides by 2. The reverse is not true.
Which method should I learn first?
The last two digits. It is the rule most textbooks print and the quickest on paper. Learn halving as well, and use it when those two digits are awkward.
What about numbers with only two digits?
Then the last two digits are the whole number, and the rule simply asks whether it is in the 4 times table.