Divisibility Rules

You can sometimes get a bit confused about simplifying fractions, finding common factors or figuring out quickly whether a large number divides by a small one (with no remainder) WITHOUT a calculator.

Take 83006509106709. Does it divide by 2?

Nah, nah, nah! I said no calculator! And before you start doing the division on paper to see if it is actually doable (you could end up with a remainder - hence lots of work for nothing), have a look at what follows - it will make your life much easier!

1. Does it divide by 2?

A number divides by 2 if it ends in an even figure (0, 2, 4, 6, 8). For instance, 2536 divides by 2 because it ends in 6, and 6 is even. 83006509106709 does NOT divide by 2 because it ends in 9, which is not even. #59;

See how easy that is? It saves lots of time and also saves you of an irrelevant division! 83006509106709 does not divide by 2, so there is no point in actually checking it by doing all the hard work.

2. Does it divide by 3?

A number divides by 3 if the sum of all its figures divides by 3. For instance, 73349 does NOT divide by 3 because 7+3+3+4+9=26 and 26 does not divide by 3 (26:3=8 remainder 2 - we don`t want remainders). 83006509106709 does divide by 3 because 8+3+0+0+6+5+0+9+1+0+6+7+0+9=54, which divides by 3 (you can check that 54 divides by 3 by adding its figures too: 5+4=9, and we know 9 divides by 3).

3. Does it divide by 5?

A number divides by 5 if it ends in 5 or 0. For instance, 560 divides by 5 because it ends in 0. Similarly, 435 divides by 5 because it ends in 5. 83006509106709 does NOT divide by 5 because it ends in 9.

4. Does it divide by 10?

Even simpler, a number divides by 10 if it ends in 0. For example, 230 divides by 10 because it ends in 0. However, 9395350682848691 does NOT divide by 10 because it ends in 1 (which is - obviously - not 0).

How awesome is that? Good luck with your exams!