Q: What are the factor combinations of the number 172,721,731?

 A:
Positive:   1 x 1727217317 x 2467453313 x 1328628791 x 18980411319 x 1309491439 x 1200299233 x 1870710073 x 17147
Negative: -1 x -172721731-7 x -24674533-13 x -13286287-91 x -1898041-1319 x -130949-1439 x -120029-9233 x -18707-10073 x -17147


How do I find the factor combinations of the number 172,721,731?

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 172,721,731, 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.

1 172,721,731
-1 -172,721,731

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 172,721,731.

Example:
1 x 172,721,731 = 172,721,731
and
-1 x -172,721,731 = 172,721,731
Notice both answers equal 172,721,731

With that explanation out of the way, let's continue. Next, we take the number 172,721,731 and divide it by 2:

172,721,731 ÷ 2 = 86,360,865.5

If the quotient is a whole number, then 2 and 86,360,865.5 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:

1 172,721,731
-1 -172,721,731

Now, we try dividing 172,721,731 by 3:

172,721,731 ÷ 3 = 57,573,910.3333

If the quotient is a whole number, then 3 and 57,573,910.3333 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:

1 172,721,731
-1 -172,721,731

Let's try dividing by 4:

172,721,731 ÷ 4 = 43,180,432.75

If the quotient is a whole number, then 4 and 43,180,432.75 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:

1 172,721,731
-1 172,721,731
Keep dividing by the next highest number until you cannot divide anymore.

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

1713911,3191,4399,23310,07317,14718,707120,029130,9491,898,04113,286,28724,674,533172,721,731
-1-7-13-91-1,319-1,439-9,233-10,073-17,147-18,707-120,029-130,949-1,898,041-13,286,287-24,674,533-172,721,731

More Examples

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