Q: What are the factor combinations of the number 101,240,321?

 A:
Positive:   1 x 1012403217 x 1446290313 x 778771717 x 595531349 x 206612991 x 1112531119 x 850759221 x 458101637 x 158933833 x 1215371547 x 654439349 x 10829
Negative: -1 x -101240321-7 x -14462903-13 x -7787717-17 x -5955313-49 x -2066129-91 x -1112531-119 x -850759-221 x -458101-637 x -158933-833 x -121537-1547 x -65443-9349 x -10829


How do I find the factor combinations of the number 101,240,321?

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 101,240,321, 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.

1 101,240,321
-1 -101,240,321

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 101,240,321.

Example:
1 x 101,240,321 = 101,240,321
and
-1 x -101,240,321 = 101,240,321
Notice both answers equal 101,240,321

With that explanation out of the way, let's continue. Next, we take the number 101,240,321 and divide it by 2:

101,240,321 ÷ 2 = 50,620,160.5

If the quotient is a whole number, then 2 and 50,620,160.5 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:

1 101,240,321
-1 -101,240,321

Now, we try dividing 101,240,321 by 3:

101,240,321 ÷ 3 = 33,746,773.6667

If the quotient is a whole number, then 3 and 33,746,773.6667 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:

1 101,240,321
-1 -101,240,321

Let's try dividing by 4:

101,240,321 ÷ 4 = 25,310,080.25

If the quotient is a whole number, then 4 and 25,310,080.25 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:

1 101,240,321
-1 101,240,321
Keep dividing by the next highest number until you cannot divide anymore.

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

17131749911192216378331,5479,34910,82965,443121,537158,933458,101850,7591,112,5312,066,1295,955,3137,787,71714,462,903101,240,321
-1-7-13-17-49-91-119-221-637-833-1,547-9,349-10,829-65,443-121,537-158,933-458,101-850,759-1,112,531-2,066,129-5,955,313-7,787,717-14,462,903-101,240,321

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