Q: What are the factor combinations of the number 10,032,625?

 A:
Positive:   1 x 100326255 x 200652525 x 40130583 x 120875125 x 80261415 x 24175967 x 103752075 x 4835
Negative: -1 x -10032625-5 x -2006525-25 x -401305-83 x -120875-125 x -80261-415 x -24175-967 x -10375-2075 x -4835


How do I find the factor combinations of the number 10,032,625?

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 10,032,625, 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 10,032,625
-1 -10,032,625

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 10,032,625.

Example:
1 x 10,032,625 = 10,032,625
and
-1 x -10,032,625 = 10,032,625
Notice both answers equal 10,032,625

With that explanation out of the way, let's continue. Next, we take the number 10,032,625 and divide it by 2:

10,032,625 ÷ 2 = 5,016,312.5

If the quotient is a whole number, then 2 and 5,016,312.5 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 10,032,625
-1 -10,032,625

Now, we try dividing 10,032,625 by 3:

10,032,625 ÷ 3 = 3,344,208.3333

If the quotient is a whole number, then 3 and 3,344,208.3333 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 10,032,625
-1 -10,032,625

Let's try dividing by 4:

10,032,625 ÷ 4 = 2,508,156.25

If the quotient is a whole number, then 4 and 2,508,156.25 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 10,032,625
-1 10,032,625
Keep dividing by the next highest number until you cannot divide anymore.

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

1525831254159672,0754,83510,37524,17580,261120,875401,3052,006,52510,032,625
-1-5-25-83-125-415-967-2,075-4,835-10,375-24,175-80,261-120,875-401,305-2,006,525-10,032,625

More Examples

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