An Introduction to Factoring

Hi, and welcome to this video lesson on factors.

Now, factors are super important to understanding how numbers are related, and most math tests are going to assume you understand these concepts, so let’s take a look.

The factors of a number are all integers by which the number can be divided.

For example:

   Factors of 18: 1, 2, 3, 6, 9, 18.

   Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.

   Common factors are all factors that are shared by both

   integers.

   Common factors of 18 and 24 are: 1, 2, 3, and 6.

The greatest common factor is the greatest factor (or biggest number) by which 18 and 24 can both be divided, and in this case, it's 6.

Make sense? Let’s try a couple of practice problems by ourselves.

Find the factors of 32 and 56, then find their common factors, then find their greatest common factor.
Practice:

   Factors of 32: 1, 2, 4, 8, 16, 32

   Factors of 56: 1, 2, 4, 8, 14, 28, 56

   Common Factors of 32 and 56: 1, 2, 4, 8

   Great Common Factor of 32 and 56: 8

Find the greatest common factor of 47 and 63

   Factors of 47: 1, 47

   Factors of 63: 1,3,7,9,21,63

That was kind of a trick question, since 47 is what we call a prime number, meaning the only factors it has are 1 and itself.

Therefore, 1 will be the greatest common factor.

We’ll talk more about prime numbers and factorization in our next video, but until then, happy studying!