Q: What are the factor combinations of the number 100,131,317?

 A:
Positive:   1 x 10013131711 x 910284713 x 770240961 x 1641497143 x 700219169 x 592493671 x 149227793 x 126269883 x 1133991859 x 538638723 x 114799713 x 10309
Negative: -1 x -100131317-11 x -9102847-13 x -7702409-61 x -1641497-143 x -700219-169 x -592493-671 x -149227-793 x -126269-883 x -113399-1859 x -53863-8723 x -11479-9713 x -10309


How do I find the factor combinations of the number 100,131,317?

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 100,131,317, 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.

1 100,131,317
-1 -100,131,317

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 100,131,317.

Example:
1 x 100,131,317 = 100,131,317
and
-1 x -100,131,317 = 100,131,317
Notice both answers equal 100,131,317

With that explanation out of the way, let's continue. Next, we take the number 100,131,317 and divide it by 2:

100,131,317 ÷ 2 = 50,065,658.5

If the quotient is a whole number, then 2 and 50,065,658.5 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:

1 100,131,317
-1 -100,131,317

Now, we try dividing 100,131,317 by 3:

100,131,317 ÷ 3 = 33,377,105.6667

If the quotient is a whole number, then 3 and 33,377,105.6667 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:

1 100,131,317
-1 -100,131,317

Let's try dividing by 4:

100,131,317 ÷ 4 = 25,032,829.25

If the quotient is a whole number, then 4 and 25,032,829.25 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:

1 100,131,317
-1 100,131,317
Keep dividing by the next highest number until you cannot divide anymore.

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

11113611431696717938831,8598,7239,71310,30911,47953,863113,399126,269149,227592,493700,2191,641,4977,702,4099,102,847100,131,317
-1-11-13-61-143-169-671-793-883-1,859-8,723-9,713-10,309-11,479-53,863-113,399-126,269-149,227-592,493-700,219-1,641,497-7,702,409-9,102,847-100,131,317

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