Q: What are the factor combinations of the number 12,444,421?

 A:
Positive:   1 x 1244442111 x 113131197 x 128293107 x 116303109 x 1141691067 x 116631177 x 105731199 x 10379
Negative: -1 x -12444421-11 x -1131311-97 x -128293-107 x -116303-109 x -114169-1067 x -11663-1177 x -10573-1199 x -10379


How do I find the factor combinations of the number 12,444,421?

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 12,444,421, 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 12,444,421
-1 -12,444,421

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 12,444,421.

Example:
1 x 12,444,421 = 12,444,421
and
-1 x -12,444,421 = 12,444,421
Notice both answers equal 12,444,421

With that explanation out of the way, let's continue. Next, we take the number 12,444,421 and divide it by 2:

12,444,421 ÷ 2 = 6,222,210.5

If the quotient is a whole number, then 2 and 6,222,210.5 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 12,444,421
-1 -12,444,421

Now, we try dividing 12,444,421 by 3:

12,444,421 ÷ 3 = 4,148,140.3333

If the quotient is a whole number, then 3 and 4,148,140.3333 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 12,444,421
-1 -12,444,421

Let's try dividing by 4:

12,444,421 ÷ 4 = 3,111,105.25

If the quotient is a whole number, then 4 and 3,111,105.25 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 12,444,421
-1 12,444,421
Keep dividing by the next highest number until you cannot divide anymore.

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

111971071091,0671,1771,19910,37910,57311,663114,169116,303128,2931,131,31112,444,421
-1-11-97-107-109-1,067-1,177-1,199-10,379-10,573-11,663-114,169-116,303-128,293-1,131,311-12,444,421

More Examples

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