Q: What are the factor combinations of the number 40,107,347?

 A:
Positive:   1 x 401073477 x 572962119 x 211091343 x 932729133 x 301559301 x 133247817 x 490915719 x 7013
Negative: -1 x -40107347-7 x -5729621-19 x -2110913-43 x -932729-133 x -301559-301 x -133247-817 x -49091-5719 x -7013


How do I find the factor combinations of the number 40,107,347?

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 40,107,347, 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 40,107,347
-1 -40,107,347

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 40,107,347.

Example:
1 x 40,107,347 = 40,107,347
and
-1 x -40,107,347 = 40,107,347
Notice both answers equal 40,107,347

With that explanation out of the way, let's continue. Next, we take the number 40,107,347 and divide it by 2:

40,107,347 ÷ 2 = 20,053,673.5

If the quotient is a whole number, then 2 and 20,053,673.5 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 40,107,347
-1 -40,107,347

Now, we try dividing 40,107,347 by 3:

40,107,347 ÷ 3 = 13,369,115.6667

If the quotient is a whole number, then 3 and 13,369,115.6667 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 40,107,347
-1 -40,107,347

Let's try dividing by 4:

40,107,347 ÷ 4 = 10,026,836.75

If the quotient is a whole number, then 4 and 10,026,836.75 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 40,107,347
-1 40,107,347
Keep dividing by the next highest number until you cannot divide anymore.

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

1719431333018175,7197,01349,091133,247301,559932,7292,110,9135,729,62140,107,347
-1-7-19-43-133-301-817-5,719-7,013-49,091-133,247-301,559-932,729-2,110,913-5,729,621-40,107,347

More Examples

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