Math Help - Factorizations, Factors and Multiples

Whether you are struggling in math class yourself, or you are helping you children it's never too late to refresh your math abilities.

Factorizations cover important basic areas in mathematics, and are not as hard as it might seem like. Just take it at your own pace and don't feel like you are "stupid" if you encounter problems. Remember that you are not meant to understand everything at first glimpse, so be kind to yourself and work hard instead of giving up too easily.

Put simply 3*5 is a factorization of 15. Every number has factorizations, and even if it's 1*15 it would still be a factorization of 15. A factorization of 20 would be 4*5, or 1*20.

Every number also has factors. The factors of a number are the numbers you would multiply in order to get that number. Factors of 15 are 1, 3, 5 and 15.

Let's say you have a number X and want to know what some of its factors are. Start by dividing X by a number m and see if you get a remainder. If you do not get a remainder, then m is a factor of X. Multiply m by the result of the division, and you end up with a factorization of X. If the division had a remainder you have to try another number until you end up with a remainder of zero.

This might be easier to see in an example, so let's say we have 27 and want to find a factorization. While this might be obvious to the naked eye, it's best to start with simple numbers instead of 45603.

Start by dividing 27 (X) with 2 (m). You will end up with a remainder, thus 2 is not a factor of 27. Now try dividing 27 (X) with 3 (m). The result of this calculation is 9, which means that 3 and 9 are factors of 27. A factorization of 27 is 3*9.

To take this a little further you would also say that 27 is a multiple of 3 and 9. The result of any number multiplied with another natural number will be a multiple of those numbers.

Other multiples of 3 would be 3, 6, 9, 12, 15 etc.

If you got through this information without a problem that's great! However if you struggled you should think of it in the simple terms of factorization, factors and multiples, and then go through them one by one. Math doesn't necessarily have to be overwhelmingly hard.