Q: What are the factor combinations of the number 12,398,155?

 A:
Positive:   1 x 123981555 x 24796317 x 177116511 x 112710535 x 35423355 x 22542177 x 161015385 x 32203
Negative: -1 x -12398155-5 x -2479631-7 x -1771165-11 x -1127105-35 x -354233-55 x -225421-77 x -161015-385 x -32203


How do I find the factor combinations of the number 12,398,155?

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 12,398,155, 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 12,398,155
-1 -12,398,155

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 12,398,155.

Example:
1 x 12,398,155 = 12,398,155
and
-1 x -12,398,155 = 12,398,155
Notice both answers equal 12,398,155

With that explanation out of the way, let's continue. Next, we take the number 12,398,155 and divide it by 2:

12,398,155 ÷ 2 = 6,199,077.5

If the quotient is a whole number, then 2 and 6,199,077.5 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 12,398,155
-1 -12,398,155

Now, we try dividing 12,398,155 by 3:

12,398,155 ÷ 3 = 4,132,718.3333

If the quotient is a whole number, then 3 and 4,132,718.3333 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 12,398,155
-1 -12,398,155

Let's try dividing by 4:

12,398,155 ÷ 4 = 3,099,538.75

If the quotient is a whole number, then 4 and 3,099,538.75 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 12,398,155
-1 12,398,155
Keep dividing by the next highest number until you cannot divide anymore.

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

1571135557738532,203161,015225,421354,2331,127,1051,771,1652,479,63112,398,155
-1-5-7-11-35-55-77-385-32,203-161,015-225,421-354,233-1,127,105-1,771,165-2,479,631-12,398,155

More Examples

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