Q: What are the factor combinations of the number 72,174,877?

 A:
Positive:   1 x 7217487717 x 424558159 x 1223303227 x 317951317 x 2276811003 x 719593859 x 187035389 x 13393
Negative: -1 x -72174877-17 x -4245581-59 x -1223303-227 x -317951-317 x -227681-1003 x -71959-3859 x -18703-5389 x -13393


How do I find the factor combinations of the number 72,174,877?

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 72,174,877, 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 72,174,877
-1 -72,174,877

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 72,174,877.

Example:
1 x 72,174,877 = 72,174,877
and
-1 x -72,174,877 = 72,174,877
Notice both answers equal 72,174,877

With that explanation out of the way, let's continue. Next, we take the number 72,174,877 and divide it by 2:

72,174,877 ÷ 2 = 36,087,438.5

If the quotient is a whole number, then 2 and 36,087,438.5 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 72,174,877
-1 -72,174,877

Now, we try dividing 72,174,877 by 3:

72,174,877 ÷ 3 = 24,058,292.3333

If the quotient is a whole number, then 3 and 24,058,292.3333 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 72,174,877
-1 -72,174,877

Let's try dividing by 4:

72,174,877 ÷ 4 = 18,043,719.25

If the quotient is a whole number, then 4 and 18,043,719.25 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 72,174,877
-1 72,174,877
Keep dividing by the next highest number until you cannot divide anymore.

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

117592273171,0033,8595,38913,39318,70371,959227,681317,9511,223,3034,245,58172,174,877
-1-17-59-227-317-1,003-3,859-5,389-13,393-18,703-71,959-227,681-317,951-1,223,303-4,245,581-72,174,877

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