# Q: What are the factor combinations of the number 542,157?

A:
Positive:   1 x 5421573 x 1807197 x 7745111 x 4928721 x 2581733 x 1642977 x 7041231 x 2347
Negative: -1 x -542157-3 x -180719-7 x -77451-11 x -49287-21 x -25817-33 x -16429-77 x -7041-231 x -2347

## How do I find the factor combinations of the number 542,157?

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 542,157, 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.

 1 542,157 -1 -542,157

#### 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 542,157.

Example:
1 x 542,157 = 542,157
and
-1 x -542,157 = 542,157

With that explanation out of the way, let's continue. Next, we take the number 542,157 and divide it by 2:

542,157 ÷ 2 = 271,078.5

If the quotient is a whole number, then 2 and 271,078.5 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

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

 1 542,157 -1 -542,157

Now, we try dividing 542,157 by 3:

542,157 ÷ 3 = 180,719

If the quotient is a whole number, then 3 and 180,719 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 3 180,719 542,157 -1 -3 -180,719 -542,157

Let's try dividing by 4:

542,157 ÷ 4 = 135,539.25

If the quotient is a whole number, then 4 and 135,539.25 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

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

 1 3 180,719 542,157 -1 -3 -180,719 542,157
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 3 7 11 21 33 77 231 2,347 7,041 16,429 25,817 49,287 77,451 180,719 542,157 -1 -3 -7 -11 -21 -33 -77 -231 -2,347 -7,041 -16,429 -25,817 -49,287 -77,451 -180,719 -542,157

### More Examples

Here are some more numbers to try:

Try the factor calculator

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