Divisibility & remainders

You want to share 20 gummy bears fairly among 4 friends? No problem, it works out evenly. With 21, one is left over. Whether a number can be shared without a remainder is a question you run into all the time: forming teams, splitting money, packing boxes. Here you'll learn to see it at a glance.

Divisible means: remainder 0

A number is divisible by another if nothing is left over when you divide. 15 is divisible by 5, because 15 divided by 5 is 3 with remainder 0. 16 is not: 16 divided by 5 is 3, but remainder 1 is left. So the remainder is what stays behind after fair sharing. It is always smaller than the number you divide by. Turned around, we say: 15 is a multiple of 5, because 5 times 3 is exactly 15. The multiples of 5 are 5, 10, 15, 20 and so on, and those are precisely the numbers where division by 5 leaves no remainder.

Rules for 2, 5 and 10

For some divisors you don't need to calculate at all, one look at the last digit is enough. Divisible by 2 are all numbers ending in 0, 2, 4, 6 or 8: those are the even numbers. All others are called odd. Divisible by 5 are numbers ending in 0 or 5. Divisible by 10 are numbers ending in 0. So for 370 you can see right away: divisible by 2, by 5 and by 10.

The digit sum reveals the 3

For 3 there is a surprising trick: add up all the digits, that's called the digit sum. If the digit sum is divisible by 3, then so is the number itself. Example 141: the digit sum is 1 + 4 + 1 = 6, and 6 is divisible by 3, so 141 is divisible by 3 too. For 142 the digit sum is 7, so it doesn't work.