Q: What are the factor combinations of the number 21,967,421?

 A:
Positive:   1 x 219674217 x 3138203107 x 205303139 x 158039211 x 104111749 x 29329973 x 225771477 x 14873
Negative: -1 x -21967421-7 x -3138203-107 x -205303-139 x -158039-211 x -104111-749 x -29329-973 x -22577-1477 x -14873


How do I find the factor combinations of the number 21,967,421?

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 21,967,421, 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 21,967,421
-1 -21,967,421

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 21,967,421.

Example:
1 x 21,967,421 = 21,967,421
and
-1 x -21,967,421 = 21,967,421
Notice both answers equal 21,967,421

With that explanation out of the way, let's continue. Next, we take the number 21,967,421 and divide it by 2:

21,967,421 ÷ 2 = 10,983,710.5

If the quotient is a whole number, then 2 and 10,983,710.5 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 21,967,421
-1 -21,967,421

Now, we try dividing 21,967,421 by 3:

21,967,421 ÷ 3 = 7,322,473.6667

If the quotient is a whole number, then 3 and 7,322,473.6667 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 21,967,421
-1 -21,967,421

Let's try dividing by 4:

21,967,421 ÷ 4 = 5,491,855.25

If the quotient is a whole number, then 4 and 5,491,855.25 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 21,967,421
-1 21,967,421
Keep dividing by the next highest number until you cannot divide anymore.

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

171071392117499731,47714,87322,57729,329104,111158,039205,3033,138,20321,967,421
-1-7-107-139-211-749-973-1,477-14,873-22,577-29,329-104,111-158,039-205,303-3,138,203-21,967,421

More Examples

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