Q: What are the factor combinations of the number 131,337,317?

 A:
Positive:   1 x 13133731729 x 452887347 x 2794411167 x 786451577 x 2276211363 x 963594843 x 271197849 x 16733
Negative: -1 x -131337317-29 x -4528873-47 x -2794411-167 x -786451-577 x -227621-1363 x -96359-4843 x -27119-7849 x -16733


How do I find the factor combinations of the number 131,337,317?

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 131,337,317, 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.

1 131,337,317
-1 -131,337,317

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 131,337,317.

Example:
1 x 131,337,317 = 131,337,317
and
-1 x -131,337,317 = 131,337,317
Notice both answers equal 131,337,317

With that explanation out of the way, let's continue. Next, we take the number 131,337,317 and divide it by 2:

131,337,317 ÷ 2 = 65,668,658.5

If the quotient is a whole number, then 2 and 65,668,658.5 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:

1 131,337,317
-1 -131,337,317

Now, we try dividing 131,337,317 by 3:

131,337,317 ÷ 3 = 43,779,105.6667

If the quotient is a whole number, then 3 and 43,779,105.6667 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:

1 131,337,317
-1 -131,337,317

Let's try dividing by 4:

131,337,317 ÷ 4 = 32,834,329.25

If the quotient is a whole number, then 4 and 32,834,329.25 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:

1 131,337,317
-1 131,337,317
Keep dividing by the next highest number until you cannot divide anymore.

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

129471675771,3634,8437,84916,73327,11996,359227,621786,4512,794,4114,528,873131,337,317
-1-29-47-167-577-1,363-4,843-7,849-16,733-27,119-96,359-227,621-786,451-2,794,411-4,528,873-131,337,317

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