# Q: What are the factor combinations of the number 456?

A:
Positive:   1 x 4562 x 2283 x 1524 x 1146 x 768 x 5712 x 3819 x 24
Negative: -1 x -456-2 x -228-3 x -152-4 x -114-6 x -76-8 x -57-12 x -38-19 x -24

## How do I find the factor combinations of the number 456?

Unfortunately, there's not simple formula to identifying all of the factors of a number and it can be a tedious process when trying to identify the divisors of larger numbers. To find the factor combinations of the number 456, it is easier to work with a table - it's called factoring from the outside in.

### Outside in Factoring

We start by creating a table and writing 1 on the left side and then the number we're trying to find the factors for on the right side in a table. Then, below that, write the numbers as a negative as well.

 1 456 -1 -456

#### Why are the negative numbers included?

When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 456.

Example:
1 x 456 = 456
and
-1 x -456 = 456

With that explanation out of the way, let's continue. Next, we take the number 456 and divide it by 2:

456 ÷ 2 = 228

If the quotient is a whole number, then 2 and 228 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

 1 2 228 456 -1 -2 -228 -456

Now, we try dividing 456 by 3:

456 ÷ 3 = 152

If the quotient is a whole number, then 3 and 152 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

 1 2 3 152 228 456 -1 -2 -3 -152 -228 -456

Let's try dividing by 4:

456 ÷ 4 = 114

If the quotient is a whole number, then 4 and 114 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

 1 2 3 4 114 152 228 456 -1 -2 -3 -4 -114 -152 -228 456
Keep dividing by the next highest number until you cannot divide anymore.

If you did it right, you will end up with this table:

 1 2 3 4 6 8 12 19 24 38 57 76 114 152 228 456 -1 -2 -3 -4 -6 -8 -12 -19 -24 -38 -57 -76 -114 -152 -228 -456

### More Examples

Here are some more numbers to try:

Try the factor calculator

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