Q: What are the factor combinations of the number 72,891,637?

 A:
Positive:   1 x 728916377 x 1041309113 x 560704991 x 801007
Negative: -1 x -72891637-7 x -10413091-13 x -5607049-91 x -801007


How do I find the factor combinations of the number 72,891,637?

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 72,891,637, 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 72,891,637
-1 -72,891,637

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 72,891,637.

Example:
1 x 72,891,637 = 72,891,637
and
-1 x -72,891,637 = 72,891,637
Notice both answers equal 72,891,637

With that explanation out of the way, let's continue. Next, we take the number 72,891,637 and divide it by 2:

72,891,637 ÷ 2 = 36,445,818.5

If the quotient is a whole number, then 2 and 36,445,818.5 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 72,891,637
-1 -72,891,637

Now, we try dividing 72,891,637 by 3:

72,891,637 ÷ 3 = 24,297,212.3333

If the quotient is a whole number, then 3 and 24,297,212.3333 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 72,891,637
-1 -72,891,637

Let's try dividing by 4:

72,891,637 ÷ 4 = 18,222,909.25

If the quotient is a whole number, then 4 and 18,222,909.25 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 72,891,637
-1 72,891,637
Keep dividing by the next highest number until you cannot divide anymore.

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

171391801,0075,607,04910,413,09172,891,637
-1-7-13-91-801,007-5,607,049-10,413,091-72,891,637

More Examples

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