Q: What are the factor combinations of the number 21,370,853?

 A:
Positive:   1 x 213708537 x 305297917 x 125710947 x 454699119 x 179587329 x 64957799 x 267473821 x 5593
Negative: -1 x -21370853-7 x -3052979-17 x -1257109-47 x -454699-119 x -179587-329 x -64957-799 x -26747-3821 x -5593


How do I find the factor combinations of the number 21,370,853?

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 21,370,853, 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 21,370,853
-1 -21,370,853

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 21,370,853.

Example:
1 x 21,370,853 = 21,370,853
and
-1 x -21,370,853 = 21,370,853
Notice both answers equal 21,370,853

With that explanation out of the way, let's continue. Next, we take the number 21,370,853 and divide it by 2:

21,370,853 ÷ 2 = 10,685,426.5

If the quotient is a whole number, then 2 and 10,685,426.5 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 21,370,853
-1 -21,370,853

Now, we try dividing 21,370,853 by 3:

21,370,853 ÷ 3 = 7,123,617.6667

If the quotient is a whole number, then 3 and 7,123,617.6667 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 21,370,853
-1 -21,370,853

Let's try dividing by 4:

21,370,853 ÷ 4 = 5,342,713.25

If the quotient is a whole number, then 4 and 5,342,713.25 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 21,370,853
-1 21,370,853
Keep dividing by the next highest number until you cannot divide anymore.

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

1717471193297993,8215,59326,74764,957179,587454,6991,257,1093,052,97921,370,853
-1-7-17-47-119-329-799-3,821-5,593-26,747-64,957-179,587-454,699-1,257,109-3,052,979-21,370,853

More Examples

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