Q: What are the factor combinations of the number 21,604,117?

 A:
Positive:   1 x 2160411731 x 696907
Negative: -1 x -21604117-31 x -696907


How do I find the factor combinations of the number 21,604,117?

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 21,604,117, 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 21,604,117
-1 -21,604,117

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 21,604,117.

Example:
1 x 21,604,117 = 21,604,117
and
-1 x -21,604,117 = 21,604,117
Notice both answers equal 21,604,117

With that explanation out of the way, let's continue. Next, we take the number 21,604,117 and divide it by 2:

21,604,117 ÷ 2 = 10,802,058.5

If the quotient is a whole number, then 2 and 10,802,058.5 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 21,604,117
-1 -21,604,117

Now, we try dividing 21,604,117 by 3:

21,604,117 ÷ 3 = 7,201,372.3333

If the quotient is a whole number, then 3 and 7,201,372.3333 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 21,604,117
-1 -21,604,117

Let's try dividing by 4:

21,604,117 ÷ 4 = 5,401,029.25

If the quotient is a whole number, then 4 and 5,401,029.25 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 21,604,117
-1 21,604,117
Keep dividing by the next highest number until you cannot divide anymore.

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

131696,90721,604,117
-1-31-696,907-21,604,117

More Examples

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