Q: What are the factor combinations of the number 12,070,409?

 A:
Positive:   1 x 1207040913 x 92849329 x 416221101 x 119509317 x 38077377 x 320171313 x 91932929 x 4121
Negative: -1 x -12070409-13 x -928493-29 x -416221-101 x -119509-317 x -38077-377 x -32017-1313 x -9193-2929 x -4121


How do I find the factor combinations of the number 12,070,409?

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 12,070,409, 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 12,070,409
-1 -12,070,409

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 12,070,409.

Example:
1 x 12,070,409 = 12,070,409
and
-1 x -12,070,409 = 12,070,409
Notice both answers equal 12,070,409

With that explanation out of the way, let's continue. Next, we take the number 12,070,409 and divide it by 2:

12,070,409 ÷ 2 = 6,035,204.5

If the quotient is a whole number, then 2 and 6,035,204.5 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 12,070,409
-1 -12,070,409

Now, we try dividing 12,070,409 by 3:

12,070,409 ÷ 3 = 4,023,469.6667

If the quotient is a whole number, then 3 and 4,023,469.6667 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 12,070,409
-1 -12,070,409

Let's try dividing by 4:

12,070,409 ÷ 4 = 3,017,602.25

If the quotient is a whole number, then 4 and 3,017,602.25 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 12,070,409
-1 12,070,409
Keep dividing by the next highest number until you cannot divide anymore.

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

113291013173771,3132,9294,1219,19332,01738,077119,509416,221928,49312,070,409
-1-13-29-101-317-377-1,313-2,929-4,121-9,193-32,017-38,077-119,509-416,221-928,493-12,070,409

More Examples

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