Q: What are the factor combinations of the number 21,323,423?

 A:
Positive:   1 x 2132342311 x 193849317 x 1254319101 x 211123187 x 1140291111 x 191931129 x 188871717 x 12419
Negative: -1 x -21323423-11 x -1938493-17 x -1254319-101 x -211123-187 x -114029-1111 x -19193-1129 x -18887-1717 x -12419


How do I find the factor combinations of the number 21,323,423?

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 21,323,423, 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 21,323,423
-1 -21,323,423

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 21,323,423.

Example:
1 x 21,323,423 = 21,323,423
and
-1 x -21,323,423 = 21,323,423
Notice both answers equal 21,323,423

With that explanation out of the way, let's continue. Next, we take the number 21,323,423 and divide it by 2:

21,323,423 ÷ 2 = 10,661,711.5

If the quotient is a whole number, then 2 and 10,661,711.5 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 21,323,423
-1 -21,323,423

Now, we try dividing 21,323,423 by 3:

21,323,423 ÷ 3 = 7,107,807.6667

If the quotient is a whole number, then 3 and 7,107,807.6667 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 21,323,423
-1 -21,323,423

Let's try dividing by 4:

21,323,423 ÷ 4 = 5,330,855.75

If the quotient is a whole number, then 4 and 5,330,855.75 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 21,323,423
-1 21,323,423
Keep dividing by the next highest number until you cannot divide anymore.

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

111171011871,1111,1291,71712,41918,88719,193114,029211,1231,254,3191,938,49321,323,423
-1-11-17-101-187-1,111-1,129-1,717-12,419-18,887-19,193-114,029-211,123-1,254,319-1,938,493-21,323,423

More Examples

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