# What is the Factor?

## Factors

Hi everyone! Welcome to this Mometrix video on factors. Factors in math refer to a number or numbers that produce a given number when multiplied.

For example:

When you multiply 6 x 7 together you get 42. Well, 6 and 7 are the factors that contributed to the outcome of 42. But, those are not the only potential factors to getting 42. Like I said, factors refer to numbers that produce a given number when multiplied. So, any two numbers that I multiply together to get 42 are considered factors of 42.

Let’s see what else we have:

1 x 42 = 42

2 x 21 = 42

3 x 14 = 42

6 x 7 = 42

Since all of these numbers (1, 2, 3, 6, 7, 14, 21 and 42) can be multiplied together to get 42, they are all considered factors of 42.

Another way that we could look at this is through division.

Let’s say you are asked the question, “ is 9 a factor of 45?”

Well, to find out, you can divide 45 by 9 (9/45), and determine whether or not the remainder is zero. Like this, in other words, is your answer a whole number? If you find a number with a zero remainder, then both 9 and that number are factors of 45. Since we can see that after the division the remainder is zero, this tells us that the divisor (9) is a factor of the dividend (45). So, the answer to our question, “is 9 a factor of 45?,” is yes!

Now, let’s take a look at another one. Is 8 a factor of 45?

When we divide 45 by 8, the divisor we are left with is a remainder of 5. So, 8 is not a factor of 45. This means that there are not 8 equal parts to 45.

So, these are examples of what factors are, but there are also types of factors:

Common factors, greatest common factors, and prime factors.

These are all, exactly, what they sound like.

Common factors are factors that two numbers share, or have in common. For example, let’s look at the factors of 35 and 40.

For 35 we have:

1 x 35, because one times 35 is equal to 35

We also have 5 x 7, because 5 times 7 equals 35

That’s about it, let’s move over to 40

For 40 we have

1 x 40, because 40 times 1 is equal to 40

We also have 2 x 20 because when you multiply those you get 40.

We also have 4 x 10

And 5 x 8, all of which end up equalling 40.

Our factors for 40 are 1, 2, 4, 5, 8, 10, 20, and 40.

To determine the common factors between 35 and 40, we just need to look at each list of factors for each number and determine which ones are the same. So, in the case of 35 and 40, the only factors that they share between these two lists, are 1 and 5. So, 1 and 5 are the common factors.

The next type of factor is a **greatest common factor**. This is the highest value common factor. You look at the list of common factors, like we have here, and determine which number is largest. In the case of 35 and 40, 1 and 5 are the only factors that they have in common, and 5 has a higher value than 1, therefore, 5 is the greatest common factor.

Now, the last type of factor is a **prime factor**. A prime factor is any number that can only be divided by 1 and itself to produce a whole number.

For example, 11 is a prime factor. Because it can only be divided by 1 and itself, when you multiply itself by 1, you end up with 11. There’s no other combination of factors that will result in 11.

I hope this lesson was helpful, thanks so much for watching, and we’ll see you guys next time!