A Guide to Factoring


Factor of a number is the one that is an exact divisor of that number. One of the most important facts about factoring is that the factor of a whole number is always a whole number. Moreover, the number will be divided exactly by its factors without leaving any remainder. An example would make it more clear for you. Just like the number 8 has factors like 1,2, 4 and 8 itself. If you try to divide 8 with any of these factors, they will divide it exactly without any remainder.

The whole process of breaking down a number to its factors is called factoring. Factoring helps a lot to calculate of the factors of a particular number. The factors of various composite numbers are expressed in terms of product of prime numbers. Though factoring is a simple process yet it sometimes can be little bit hard to factorize a large number.

Different Benefits of Factoring

Composite numbers - There are also certain terms framed based on factors like the composite numbers and the prime numbers. Composite numbers are those which have factors other than 1 and the number itself. For instance, a number like 10 has 1, 2, 5, 10 as factors. Therefore, apart from having 1 and itself as a factor, it also has numbers like 2 and 5 as its factors and is thus a composite numbers.

Prime numbers – The numbers that have only 1 and itself as a factor is a prime number. For instance, 3 is a number which has only got 1 and itself as the factor. Therefore, it is a prime number. However, 2 is the only even prime number available.


Calculating Highest Common Factor or H.C.F

There may be two numbers that share the same factors. For instance the two numbers 21 and 9 share same factor 3. There may be more than one same factor. These factors are called common factors. However, there are also some other things attached to factoring. Factoring also helps you to find out the H.C.F or the Highest Common Factor. For instance, the number 24 has factors like 1, 2, 3, 4, 6, 8, 12 and 24 whereas the number 36 has factors like 1, 2, 3, 4, 6, 9, 12, 18 and 36. These two have several common factors like 1, 2, 3, 4, 6, 12. However, the highest common factor is 12 and hence the H.C.F of 24 and 36 is 12.

Algebra: In fact, factoring is also used in algebra as well as factors of algebraic expression are themselves expressions. When these expressions are multiplied together, they form the original expression. For instance, (x – y) and (x + y) are the factors of x2 – y2 as when (x – y) and (x + y) are multiplied to each other it gives x2 – y2. Thus, factoring is also an indispensable part of algebra.