What is the division rule for 4?

Answer 1

If the last two digits of a number are divisible by 4, the entire number is divisible by 4. The reason this works is because 100 is a multiple of 4.
For a number to be divisible by 4, the number formed by the last two digits should be divisible by 4.

For example:

324 is divisible by 4 because the last two digits put together are 24, and 24/6=4

337 is not divisible by 4 because the last two digits put together are 37, and 37 cannot be divided by 4.

Answer 2

IF the last 2 numbers are divisible by 4 and it is even.

Now how to tell if the last two digits of the number are divisible by 4: If the ones digit is a 0, 4 or 8 and the tens digit is an even number (such as 00, 04, 08, 20, 24, 28, 40, 44, etc.) OR if the ones digit is 2 or 6 and the tens digit is an odd number (such as 12, 16, 32, 36, etc).

Here is how it works (this is not a formal proof, but it'll show you). Take the first part of the criteria (last 2 digits are divisible by 4). So find two whole numbers {a & b} such that the number equals 100a + b, then the number b is the last two digits, and the number a is the digits to the left of those two digits. If you divide this by 4, you get (100a + b)/4 = 25a + b/4. So 25a is a whole number, and b/4 is a whole number if b (the last two digits) is divisible by 4.

For the second part, take {with n is a whole number, and m = 0, 1 or 2} (20n + 4m)/4 = 5n + m, which is a whole number so (20n + 4m) is divisible by 4 (this covers the even tens digit with 0,4 & 8). Now take (20n + 12), which covers 12, 32, ... 92. Divide by 4: (20n + 12)/4 = 5n + 3, so (20n + 12) is divisible by 4. Now see that (20n + 16) is divisible by 4, which takes care of 16, 36, 56, ... 96.

Answer 3

The 2-digit number formed by the last two digits is divisible by 4.