Q: What are the factor combinations of the number 37,510,921?

 A:
Positive:   1 x 375109217 x 535870319 x 197425943 x 87234749 x 765529133 x 282037301 x 124621817 x 45913931 x 40291937 x 400332107 x 178035719 x 6559
Negative: -1 x -37510921-7 x -5358703-19 x -1974259-43 x -872347-49 x -765529-133 x -282037-301 x -124621-817 x -45913-931 x -40291-937 x -40033-2107 x -17803-5719 x -6559


How do I find the factor combinations of the number 37,510,921?

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 37,510,921, 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 37,510,921
-1 -37,510,921

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 37,510,921.

Example:
1 x 37,510,921 = 37,510,921
and
-1 x -37,510,921 = 37,510,921
Notice both answers equal 37,510,921

With that explanation out of the way, let's continue. Next, we take the number 37,510,921 and divide it by 2:

37,510,921 ÷ 2 = 18,755,460.5

If the quotient is a whole number, then 2 and 18,755,460.5 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 37,510,921
-1 -37,510,921

Now, we try dividing 37,510,921 by 3:

37,510,921 ÷ 3 = 12,503,640.3333

If the quotient is a whole number, then 3 and 12,503,640.3333 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 37,510,921
-1 -37,510,921

Let's try dividing by 4:

37,510,921 ÷ 4 = 9,377,730.25

If the quotient is a whole number, then 4 and 9,377,730.25 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 37,510,921
-1 37,510,921
Keep dividing by the next highest number until you cannot divide anymore.

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

171943491333018179319372,1075,7196,55917,80340,03340,29145,913124,621282,037765,529872,3471,974,2595,358,70337,510,921
-1-7-19-43-49-133-301-817-931-937-2,107-5,719-6,559-17,803-40,033-40,291-45,913-124,621-282,037-765,529-872,347-1,974,259-5,358,703-37,510,921

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