Q: What are the factor combinations of the number 12,117,175?

 A:
Positive:   1 x 121171755 x 24234357 x 173102517 x 71277525 x 48468735 x 34620585 x 142555119 x 101825175 x 69241425 x 28511595 x 203652975 x 4073
Negative: -1 x -12117175-5 x -2423435-7 x -1731025-17 x -712775-25 x -484687-35 x -346205-85 x -142555-119 x -101825-175 x -69241-425 x -28511-595 x -20365-2975 x -4073


How do I find the factor combinations of the number 12,117,175?

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 12,117,175, 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 12,117,175
-1 -12,117,175

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 12,117,175.

Example:
1 x 12,117,175 = 12,117,175
and
-1 x -12,117,175 = 12,117,175
Notice both answers equal 12,117,175

With that explanation out of the way, let's continue. Next, we take the number 12,117,175 and divide it by 2:

12,117,175 ÷ 2 = 6,058,587.5

If the quotient is a whole number, then 2 and 6,058,587.5 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 12,117,175
-1 -12,117,175

Now, we try dividing 12,117,175 by 3:

12,117,175 ÷ 3 = 4,039,058.3333

If the quotient is a whole number, then 3 and 4,039,058.3333 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 12,117,175
-1 -12,117,175

Let's try dividing by 4:

12,117,175 ÷ 4 = 3,029,293.75

If the quotient is a whole number, then 4 and 3,029,293.75 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 12,117,175
-1 12,117,175
Keep dividing by the next highest number until you cannot divide anymore.

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

157172535851191754255952,9754,07320,36528,51169,241101,825142,555346,205484,687712,7751,731,0252,423,43512,117,175
-1-5-7-17-25-35-85-119-175-425-595-2,975-4,073-20,365-28,511-69,241-101,825-142,555-346,205-484,687-712,775-1,731,025-2,423,435-12,117,175

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