Is 968 divisible by 4

Answer 1

Yes, you can tell (without actually doing the division).

• First, of course the number needs to be an even number, if not then you can stop.
• If the tens digit (6 in this example) is even {0,2,4,6,8}, then look at the ones digit (4 in the example). If the ones digit is {0,4, or 8}, then the whole number is divisible by 4.
• If the tens digit is odd {1,3,5,7,9}, then look at ones digit. If ones digit is {2 or 6}, then the whole number is divisible by 4.

So numbers ending in 32, 36, 52, 24, 04, .... and like this example 68 are all divisible by 4. Why this works - without a true formal proof, consider this: break the number apart, to the last two digits and the rest of the number.

So our number becomes 968 = 900 + 68. So 968/4 = (900 + 68) / 4, which equals 900/4 + 68/4. Since 100 is divisible by 4, then any multiple of 100 (such as 900) is also divisible by 4, so now you only have to consider the last two digits.