Q: What are the factor combinations of the number 135,216,521?

 A:
Positive:   1 x 13521652111 x 1229241117 x 795391319 x 7116659187 x 723083209 x 646969323 x 418627361 x 3745612003 x 675073553 x 380573971 x 340516137 x 22033
Negative: -1 x -135216521-11 x -12292411-17 x -7953913-19 x -7116659-187 x -723083-209 x -646969-323 x -418627-361 x -374561-2003 x -67507-3553 x -38057-3971 x -34051-6137 x -22033


How do I find the factor combinations of the number 135,216,521?

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 135,216,521, 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.

1 135,216,521
-1 -135,216,521

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 135,216,521.

Example:
1 x 135,216,521 = 135,216,521
and
-1 x -135,216,521 = 135,216,521
Notice both answers equal 135,216,521

With that explanation out of the way, let's continue. Next, we take the number 135,216,521 and divide it by 2:

135,216,521 ÷ 2 = 67,608,260.5

If the quotient is a whole number, then 2 and 67,608,260.5 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:

1 135,216,521
-1 -135,216,521

Now, we try dividing 135,216,521 by 3:

135,216,521 ÷ 3 = 45,072,173.6667

If the quotient is a whole number, then 3 and 45,072,173.6667 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:

1 135,216,521
-1 -135,216,521

Let's try dividing by 4:

135,216,521 ÷ 4 = 33,804,130.25

If the quotient is a whole number, then 4 and 33,804,130.25 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:

1 135,216,521
-1 135,216,521
Keep dividing by the next highest number until you cannot divide anymore.

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

11117191872093233612,0033,5533,9716,13722,03334,05138,05767,507374,561418,627646,969723,0837,116,6597,953,91312,292,411135,216,521
-1-11-17-19-187-209-323-361-2,003-3,553-3,971-6,137-22,033-34,051-38,057-67,507-374,561-418,627-646,969-723,083-7,116,659-7,953,913-12,292,411-135,216,521

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