Q: What are the factor combinations of the number 21,402,199?

 A:
Positive:   1 x 214021997 x 305745713 x 164632391 x 235189479 x 44681491 x 435893353 x 63833437 x 6227
Negative: -1 x -21402199-7 x -3057457-13 x -1646323-91 x -235189-479 x -44681-491 x -43589-3353 x -6383-3437 x -6227


How do I find the factor combinations of the number 21,402,199?

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 21,402,199, 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 21,402,199
-1 -21,402,199

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 21,402,199.

Example:
1 x 21,402,199 = 21,402,199
and
-1 x -21,402,199 = 21,402,199
Notice both answers equal 21,402,199

With that explanation out of the way, let's continue. Next, we take the number 21,402,199 and divide it by 2:

21,402,199 ÷ 2 = 10,701,099.5

If the quotient is a whole number, then 2 and 10,701,099.5 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 21,402,199
-1 -21,402,199

Now, we try dividing 21,402,199 by 3:

21,402,199 ÷ 3 = 7,134,066.3333

If the quotient is a whole number, then 3 and 7,134,066.3333 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 21,402,199
-1 -21,402,199

Let's try dividing by 4:

21,402,199 ÷ 4 = 5,350,549.75

If the quotient is a whole number, then 4 and 5,350,549.75 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 21,402,199
-1 21,402,199
Keep dividing by the next highest number until you cannot divide anymore.

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

1713914794913,3533,4376,2276,38343,58944,681235,1891,646,3233,057,45721,402,199
-1-7-13-91-479-491-3,353-3,437-6,227-6,383-43,589-44,681-235,189-1,646,323-3,057,457-21,402,199

More Examples

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