100 is divisible by 4 exactly 25 times. Between 0 and 100, every other even number is divisible by 4; 4, 8, 12, 16 and so on.
However, if you look, there is a pattern to the way the numbers fall. Let's look at the first five multiples of 4: 4, 8, 12, 16, 20.
Notice how the last digits are 4, 8, 2, 6, 0. The first digits here would be 0, 1 and 2: 04, 08, 12, 16, 20. Two of the tens digit numbers are odd; the rest, even.
Now the next set of five multiples: 24, 28, 32, 36, 40. And again, it's even, even, odd, odd, even. And we see a pattern forming.
Does this pattern continue in the next set of five digits? Let's look at 44, 48, 52, 56, 60. Even, even, odd, odd, even.
That makes it three times. Definitely onto something.
So the rule for checking for divisibility by 4 should be: If the number is even, check the two rightmost digits (tens and units).
The number is divisible by 4 if:-
| Tens digit | Units digit |
|---|---|
| Even | 4, 8 or 0 |
| Odd | 2 or 6 |
This test works whether the number is 16, 76 or 3,465,234,772,236: if the last two digits fit the pattern in the table above, it is divisible by 4.
Try it for yourself with the following numbers:-
456
364
394
3,766
4,966
4,632
58,646
57,638
294,576
3,944,858
29,338,476
29,445,674
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