Q: What are the factor combinations of the number 131,232,605?

 A:
Positive:   1 x 1312326055 x 262465217 x 1874751517 x 771956535 x 374950385 x 1543913119 x 1102795595 x 220559
Negative: -1 x -131232605-5 x -26246521-7 x -18747515-17 x -7719565-35 x -3749503-85 x -1543913-119 x -1102795-595 x -220559


How do I find the factor combinations of the number 131,232,605?

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 131,232,605, 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.

1 131,232,605
-1 -131,232,605

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 131,232,605.

Example:
1 x 131,232,605 = 131,232,605
and
-1 x -131,232,605 = 131,232,605
Notice both answers equal 131,232,605

With that explanation out of the way, let's continue. Next, we take the number 131,232,605 and divide it by 2:

131,232,605 ÷ 2 = 65,616,302.5

If the quotient is a whole number, then 2 and 65,616,302.5 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:

1 131,232,605
-1 -131,232,605

Now, we try dividing 131,232,605 by 3:

131,232,605 ÷ 3 = 43,744,201.6667

If the quotient is a whole number, then 3 and 43,744,201.6667 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:

1 131,232,605
-1 -131,232,605

Let's try dividing by 4:

131,232,605 ÷ 4 = 32,808,151.25

If the quotient is a whole number, then 4 and 32,808,151.25 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:

1 131,232,605
-1 131,232,605
Keep dividing by the next highest number until you cannot divide anymore.

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

157173585119595220,5591,102,7951,543,9133,749,5037,719,56518,747,51526,246,521131,232,605
-1-5-7-17-35-85-119-595-220,559-1,102,795-1,543,913-3,749,503-7,719,565-18,747,515-26,246,521-131,232,605

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