Q: What are the factor combinations of the number 172,064,225?

 A:
Positive:   1 x 1720642255 x 3441284517 x 1012142525 x 688256961 x 282072585 x 2024285305 x 564145425 x 4048571037 x 1659251525 x 1128295185 x 331856637 x 25925
Negative: -1 x -172064225-5 x -34412845-17 x -10121425-25 x -6882569-61 x -2820725-85 x -2024285-305 x -564145-425 x -404857-1037 x -165925-1525 x -112829-5185 x -33185-6637 x -25925


How do I find the factor combinations of the number 172,064,225?

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 172,064,225, 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.

1 172,064,225
-1 -172,064,225

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 172,064,225.

Example:
1 x 172,064,225 = 172,064,225
and
-1 x -172,064,225 = 172,064,225
Notice both answers equal 172,064,225

With that explanation out of the way, let's continue. Next, we take the number 172,064,225 and divide it by 2:

172,064,225 ÷ 2 = 86,032,112.5

If the quotient is a whole number, then 2 and 86,032,112.5 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:

1 172,064,225
-1 -172,064,225

Now, we try dividing 172,064,225 by 3:

172,064,225 ÷ 3 = 57,354,741.6667

If the quotient is a whole number, then 3 and 57,354,741.6667 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:

1 172,064,225
-1 -172,064,225

Let's try dividing by 4:

172,064,225 ÷ 4 = 43,016,056.25

If the quotient is a whole number, then 4 and 43,016,056.25 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:

1 172,064,225
-1 172,064,225
Keep dividing by the next highest number until you cannot divide anymore.

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

15172561853054251,0371,5255,1856,63725,92533,185112,829165,925404,857564,1452,024,2852,820,7256,882,56910,121,42534,412,845172,064,225
-1-5-17-25-61-85-305-425-1,037-1,525-5,185-6,637-25,925-33,185-112,829-165,925-404,857-564,145-2,024,285-2,820,725-6,882,569-10,121,425-34,412,845-172,064,225

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