Q: What are the factor combinations of the number 21,132,139?

 A:
Positive:   1 x 211321397 x 301887717 x 1243067119 x 177581311 x 67949571 x 370092177 x 97073997 x 5287
Negative: -1 x -21132139-7 x -3018877-17 x -1243067-119 x -177581-311 x -67949-571 x -37009-2177 x -9707-3997 x -5287


How do I find the factor combinations of the number 21,132,139?

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 21,132,139, 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 21,132,139
-1 -21,132,139

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 21,132,139.

Example:
1 x 21,132,139 = 21,132,139
and
-1 x -21,132,139 = 21,132,139
Notice both answers equal 21,132,139

With that explanation out of the way, let's continue. Next, we take the number 21,132,139 and divide it by 2:

21,132,139 ÷ 2 = 10,566,069.5

If the quotient is a whole number, then 2 and 10,566,069.5 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 21,132,139
-1 -21,132,139

Now, we try dividing 21,132,139 by 3:

21,132,139 ÷ 3 = 7,044,046.3333

If the quotient is a whole number, then 3 and 7,044,046.3333 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 21,132,139
-1 -21,132,139

Let's try dividing by 4:

21,132,139 ÷ 4 = 5,283,034.75

If the quotient is a whole number, then 4 and 5,283,034.75 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 21,132,139
-1 21,132,139
Keep dividing by the next highest number until you cannot divide anymore.

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

17171193115712,1773,9975,2879,70737,00967,949177,5811,243,0673,018,87721,132,139
-1-7-17-119-311-571-2,177-3,997-5,287-9,707-37,009-67,949-177,581-1,243,067-3,018,877-21,132,139

More Examples

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