Q: What are the factor combinations of the number 12,700,135?

 A:
Positive:   1 x 127001355 x 25400277 x 181430535 x 362861109 x 116515545 x 23303763 x 166453329 x 3815
Negative: -1 x -12700135-5 x -2540027-7 x -1814305-35 x -362861-109 x -116515-545 x -23303-763 x -16645-3329 x -3815


How do I find the factor combinations of the number 12,700,135?

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 12,700,135, 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 12,700,135
-1 -12,700,135

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 12,700,135.

Example:
1 x 12,700,135 = 12,700,135
and
-1 x -12,700,135 = 12,700,135
Notice both answers equal 12,700,135

With that explanation out of the way, let's continue. Next, we take the number 12,700,135 and divide it by 2:

12,700,135 ÷ 2 = 6,350,067.5

If the quotient is a whole number, then 2 and 6,350,067.5 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 12,700,135
-1 -12,700,135

Now, we try dividing 12,700,135 by 3:

12,700,135 ÷ 3 = 4,233,378.3333

If the quotient is a whole number, then 3 and 4,233,378.3333 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 12,700,135
-1 -12,700,135

Let's try dividing by 4:

12,700,135 ÷ 4 = 3,175,033.75

If the quotient is a whole number, then 4 and 3,175,033.75 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 12,700,135
-1 12,700,135
Keep dividing by the next highest number until you cannot divide anymore.

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

157351095457633,3293,81516,64523,303116,515362,8611,814,3052,540,02712,700,135
-1-5-7-35-109-545-763-3,329-3,815-16,645-23,303-116,515-362,861-1,814,305-2,540,027-12,700,135

More Examples

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