Q: What are the factor combinations of the number 12,359,825?

 A:
Positive:   1 x 123598255 x 247196525 x 49439347 x 26297567 x 184475157 x 78725235 x 52595335 x 36895785 x 157451175 x 105191675 x 73793149 x 3925
Negative: -1 x -12359825-5 x -2471965-25 x -494393-47 x -262975-67 x -184475-157 x -78725-235 x -52595-335 x -36895-785 x -15745-1175 x -10519-1675 x -7379-3149 x -3925


How do I find the factor combinations of the number 12,359,825?

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 12,359,825, 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 12,359,825
-1 -12,359,825

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 12,359,825.

Example:
1 x 12,359,825 = 12,359,825
and
-1 x -12,359,825 = 12,359,825
Notice both answers equal 12,359,825

With that explanation out of the way, let's continue. Next, we take the number 12,359,825 and divide it by 2:

12,359,825 ÷ 2 = 6,179,912.5

If the quotient is a whole number, then 2 and 6,179,912.5 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 12,359,825
-1 -12,359,825

Now, we try dividing 12,359,825 by 3:

12,359,825 ÷ 3 = 4,119,941.6667

If the quotient is a whole number, then 3 and 4,119,941.6667 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 12,359,825
-1 -12,359,825

Let's try dividing by 4:

12,359,825 ÷ 4 = 3,089,956.25

If the quotient is a whole number, then 4 and 3,089,956.25 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 12,359,825
-1 12,359,825
Keep dividing by the next highest number until you cannot divide anymore.

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

152547671572353357851,1751,6753,1493,9257,37910,51915,74536,89552,59578,725184,475262,975494,3932,471,96512,359,825
-1-5-25-47-67-157-235-335-785-1,175-1,675-3,149-3,925-7,379-10,519-15,745-36,895-52,595-78,725-184,475-262,975-494,393-2,471,965-12,359,825

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