Q: What are the factor combinations of the number 21,409,933?

 A:
Positive:   1 x 2140993331 x 69064353 x 40396183 x 257951157 x 1363691643 x 130312573 x 83214399 x 4867
Negative: -1 x -21409933-31 x -690643-53 x -403961-83 x -257951-157 x -136369-1643 x -13031-2573 x -8321-4399 x -4867


How do I find the factor combinations of the number 21,409,933?

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 21,409,933, 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 21,409,933
-1 -21,409,933

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 21,409,933.

Example:
1 x 21,409,933 = 21,409,933
and
-1 x -21,409,933 = 21,409,933
Notice both answers equal 21,409,933

With that explanation out of the way, let's continue. Next, we take the number 21,409,933 and divide it by 2:

21,409,933 ÷ 2 = 10,704,966.5

If the quotient is a whole number, then 2 and 10,704,966.5 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 21,409,933
-1 -21,409,933

Now, we try dividing 21,409,933 by 3:

21,409,933 ÷ 3 = 7,136,644.3333

If the quotient is a whole number, then 3 and 7,136,644.3333 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 21,409,933
-1 -21,409,933

Let's try dividing by 4:

21,409,933 ÷ 4 = 5,352,483.25

If the quotient is a whole number, then 4 and 5,352,483.25 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 21,409,933
-1 21,409,933
Keep dividing by the next highest number until you cannot divide anymore.

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

13153831571,6432,5734,3994,8678,32113,031136,369257,951403,961690,64321,409,933
-1-31-53-83-157-1,643-2,573-4,399-4,867-8,321-13,031-136,369-257,951-403,961-690,643-21,409,933

More Examples

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