Q: What are the factor combinations of the number 21,807,617?

 A:
Positive:   1 x 2180761713 x 167750917 x 1282801101 x 215917221 x 98677977 x 223211313 x 166091717 x 12701
Negative: -1 x -21807617-13 x -1677509-17 x -1282801-101 x -215917-221 x -98677-977 x -22321-1313 x -16609-1717 x -12701


How do I find the factor combinations of the number 21,807,617?

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 21,807,617, 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 21,807,617
-1 -21,807,617

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 21,807,617.

Example:
1 x 21,807,617 = 21,807,617
and
-1 x -21,807,617 = 21,807,617
Notice both answers equal 21,807,617

With that explanation out of the way, let's continue. Next, we take the number 21,807,617 and divide it by 2:

21,807,617 ÷ 2 = 10,903,808.5

If the quotient is a whole number, then 2 and 10,903,808.5 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 21,807,617
-1 -21,807,617

Now, we try dividing 21,807,617 by 3:

21,807,617 ÷ 3 = 7,269,205.6667

If the quotient is a whole number, then 3 and 7,269,205.6667 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 21,807,617
-1 -21,807,617

Let's try dividing by 4:

21,807,617 ÷ 4 = 5,451,904.25

If the quotient is a whole number, then 4 and 5,451,904.25 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 21,807,617
-1 21,807,617
Keep dividing by the next highest number until you cannot divide anymore.

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

113171012219771,3131,71712,70116,60922,32198,677215,9171,282,8011,677,50921,807,617
-1-13-17-101-221-977-1,313-1,717-12,701-16,609-22,321-98,677-215,917-1,282,801-1,677,509-21,807,617

More Examples

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