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. There are two good tests, and which one is easier depends on the number in front of you.
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, and it is the method that scales to 8, where you halve three times.
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 it goes wrong
- Checking only the last digit. Even is necessary but not sufficient: 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 a child learn first?
The last-two-digits rule is the one in most textbooks and is quickest on paper. Halving twice is worth showing as well, because it explains why the rule for 8 is halving three times.
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.