Q: What are the factor combinations of the number 37,904,009?

 A:
Positive:   1 x 3790400911 x 344581913 x 291569373 x 519233143 x 265063803 x 47203949 x 399413631 x 10439
Negative: -1 x -37904009-11 x -3445819-13 x -2915693-73 x -519233-143 x -265063-803 x -47203-949 x -39941-3631 x -10439


How do I find the factor combinations of the number 37,904,009?

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 37,904,009, 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 37,904,009
-1 -37,904,009

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 37,904,009.

Example:
1 x 37,904,009 = 37,904,009
and
-1 x -37,904,009 = 37,904,009
Notice both answers equal 37,904,009

With that explanation out of the way, let's continue. Next, we take the number 37,904,009 and divide it by 2:

37,904,009 ÷ 2 = 18,952,004.5

If the quotient is a whole number, then 2 and 18,952,004.5 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 37,904,009
-1 -37,904,009

Now, we try dividing 37,904,009 by 3:

37,904,009 ÷ 3 = 12,634,669.6667

If the quotient is a whole number, then 3 and 12,634,669.6667 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 37,904,009
-1 -37,904,009

Let's try dividing by 4:

37,904,009 ÷ 4 = 9,476,002.25

If the quotient is a whole number, then 4 and 9,476,002.25 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 37,904,009
-1 37,904,009
Keep dividing by the next highest number until you cannot divide anymore.

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

11113731438039493,63110,43939,94147,203265,063519,2332,915,6933,445,81937,904,009
-1-11-13-73-143-803-949-3,631-10,439-39,941-47,203-265,063-519,233-2,915,693-3,445,819-37,904,009

More Examples

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