Q: What are the factor combinations of the number 12,438,629?

 A:
Positive:   1 x 124386297 x 177694779 x 15745183 x 149863271 x 45899553 x 22493581 x 214091897 x 6557
Negative: -1 x -12438629-7 x -1776947-79 x -157451-83 x -149863-271 x -45899-553 x -22493-581 x -21409-1897 x -6557


How do I find the factor combinations of the number 12,438,629?

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 12,438,629, 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 12,438,629
-1 -12,438,629

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 12,438,629.

Example:
1 x 12,438,629 = 12,438,629
and
-1 x -12,438,629 = 12,438,629
Notice both answers equal 12,438,629

With that explanation out of the way, let's continue. Next, we take the number 12,438,629 and divide it by 2:

12,438,629 ÷ 2 = 6,219,314.5

If the quotient is a whole number, then 2 and 6,219,314.5 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 12,438,629
-1 -12,438,629

Now, we try dividing 12,438,629 by 3:

12,438,629 ÷ 3 = 4,146,209.6667

If the quotient is a whole number, then 3 and 4,146,209.6667 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 12,438,629
-1 -12,438,629

Let's try dividing by 4:

12,438,629 ÷ 4 = 3,109,657.25

If the quotient is a whole number, then 4 and 3,109,657.25 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 12,438,629
-1 12,438,629
Keep dividing by the next highest number until you cannot divide anymore.

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

1779832715535811,8976,55721,40922,49345,899149,863157,4511,776,94712,438,629
-1-7-79-83-271-553-581-1,897-6,557-21,409-22,493-45,899-149,863-157,451-1,776,947-12,438,629

More Examples

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