Q: What are the factor combinations of the number 437,657,317?

 A:
Positive:   1 x 43765731723 x 19028579199 x 21992834577 x 95621
Negative: -1 x -437657317-23 x -19028579-199 x -2199283-4577 x -95621


How do I find the factor combinations of the number 437,657,317?

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 437,657,317, 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.

1 437,657,317
-1 -437,657,317

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 437,657,317.

Example:
1 x 437,657,317 = 437,657,317
and
-1 x -437,657,317 = 437,657,317
Notice both answers equal 437,657,317

With that explanation out of the way, let's continue. Next, we take the number 437,657,317 and divide it by 2:

437,657,317 ÷ 2 = 218,828,658.5

If the quotient is a whole number, then 2 and 218,828,658.5 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:

1 437,657,317
-1 -437,657,317

Now, we try dividing 437,657,317 by 3:

437,657,317 ÷ 3 = 145,885,772.3333

If the quotient is a whole number, then 3 and 145,885,772.3333 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:

1 437,657,317
-1 -437,657,317

Let's try dividing by 4:

437,657,317 ÷ 4 = 109,414,329.25

If the quotient is a whole number, then 4 and 109,414,329.25 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:

1 437,657,317
-1 437,657,317
Keep dividing by the next highest number until you cannot divide anymore.

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

1231994,57795,6212,199,28319,028,579437,657,317
-1-23-199-4,577-95,621-2,199,283-19,028,579-437,657,317

More Examples

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