Q: What are the factor combinations of the number 172,506,529?

 A:
Positive:   1 x 17250652913 x 1326973319 x 907929129 x 5948501247 x 698407377 x 457577551 x 3130797163 x 24083
Negative: -1 x -172506529-13 x -13269733-19 x -9079291-29 x -5948501-247 x -698407-377 x -457577-551 x -313079-7163 x -24083


How do I find the factor combinations of the number 172,506,529?

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 172,506,529, 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.

1 172,506,529
-1 -172,506,529

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 172,506,529.

Example:
1 x 172,506,529 = 172,506,529
and
-1 x -172,506,529 = 172,506,529
Notice both answers equal 172,506,529

With that explanation out of the way, let's continue. Next, we take the number 172,506,529 and divide it by 2:

172,506,529 ÷ 2 = 86,253,264.5

If the quotient is a whole number, then 2 and 86,253,264.5 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:

1 172,506,529
-1 -172,506,529

Now, we try dividing 172,506,529 by 3:

172,506,529 ÷ 3 = 57,502,176.3333

If the quotient is a whole number, then 3 and 57,502,176.3333 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:

1 172,506,529
-1 -172,506,529

Let's try dividing by 4:

172,506,529 ÷ 4 = 43,126,632.25

If the quotient is a whole number, then 4 and 43,126,632.25 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:

1 172,506,529
-1 172,506,529
Keep dividing by the next highest number until you cannot divide anymore.

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

11319292473775517,16324,083313,079457,577698,4075,948,5019,079,29113,269,733172,506,529
-1-13-19-29-247-377-551-7,163-24,083-313,079-457,577-698,407-5,948,501-9,079,291-13,269,733-172,506,529

More Examples

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