How do you know a number is divisible by 4?

Answer 1

If a number can be divisible by 2 twice( ei, 48 in half is 24 and 24 can be divided in half.

But you can check, without doing any dividing. If the last 2 digits (the tens and ones place digits) is divisible by 4, then the whole number is divisible by 4.

How to tell if the last two digits are divisible by 4: add the ones digit to twice the tens digit: if this sum is divisible by 4, then so is the original. This sum can be repeated until a single digit remains. IF this digit is 4 or 8, then the original number is divisible by 4.

So if you have a number 975239806723498658859303524, then the last two digits are 24, which is divisible by 4 and the entire number is divisible by 4 (4 + 2×2 = 8 which is 4 or 8, so 24 is divisible by 4).

Why this works: Suppose you have a whole number M. Rewrite the number as M = 100*P + Q, where P & Q are whole numbers. Note that Q represents the last two digits, and P is the rest of the number. Now divide this by 4: M/4 = (100*P + Q)/4 = 100*P/4 + Q/4 = 25*P + Q/4. So since P is a whole number, then 25*P is a whole number, and if Q/4 is a whole number, then [M/4 = 25*P + Q/4], which is the sum of two whole numbers is also a whole number, so M is divisible by 4.

Let M = 324, so P = 3, and Q = 24. 324 = 100*3 + 24, and 324/4 = 25*3 + 24/4 = 75 + 6 = 81. So 324 is divisible by 4.

A number which is divisible by 4 is a multiple of 4