Q: What are the factor combinations of the number 21,493,633?

 A:
Positive:   1 x 214936337 x 307051931 x 69334337 x 580909217 x 99049259 x 829871147 x 187392677 x 8029
Negative: -1 x -21493633-7 x -3070519-31 x -693343-37 x -580909-217 x -99049-259 x -82987-1147 x -18739-2677 x -8029


How do I find the factor combinations of the number 21,493,633?

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 21,493,633, 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 21,493,633
-1 -21,493,633

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 21,493,633.

Example:
1 x 21,493,633 = 21,493,633
and
-1 x -21,493,633 = 21,493,633
Notice both answers equal 21,493,633

With that explanation out of the way, let's continue. Next, we take the number 21,493,633 and divide it by 2:

21,493,633 ÷ 2 = 10,746,816.5

If the quotient is a whole number, then 2 and 10,746,816.5 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 21,493,633
-1 -21,493,633

Now, we try dividing 21,493,633 by 3:

21,493,633 ÷ 3 = 7,164,544.3333

If the quotient is a whole number, then 3 and 7,164,544.3333 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 21,493,633
-1 -21,493,633

Let's try dividing by 4:

21,493,633 ÷ 4 = 5,373,408.25

If the quotient is a whole number, then 4 and 5,373,408.25 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 21,493,633
-1 21,493,633
Keep dividing by the next highest number until you cannot divide anymore.

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

1731372172591,1472,6778,02918,73982,98799,049580,909693,3433,070,51921,493,633
-1-7-31-37-217-259-1,147-2,677-8,029-18,739-82,987-99,049-580,909-693,343-3,070,519-21,493,633

More Examples

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