Q: What are the factor combinations of the number 7,531,825?

 A:
Positive:   1 x 75318255 x 15063657 x 107597525 x 30127335 x 215195175 x 43039193 x 39025223 x 33775965 x 78051115 x 67551351 x 55751561 x 4825
Negative: -1 x -7531825-5 x -1506365-7 x -1075975-25 x -301273-35 x -215195-175 x -43039-193 x -39025-223 x -33775-965 x -7805-1115 x -6755-1351 x -5575-1561 x -4825


How do I find the factor combinations of the number 7,531,825?

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 7,531,825, 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 7,531,825
-1 -7,531,825

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 7,531,825.

Example:
1 x 7,531,825 = 7,531,825
and
-1 x -7,531,825 = 7,531,825
Notice both answers equal 7,531,825

With that explanation out of the way, let's continue. Next, we take the number 7,531,825 and divide it by 2:

7,531,825 ÷ 2 = 3,765,912.5

If the quotient is a whole number, then 2 and 3,765,912.5 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 7,531,825
-1 -7,531,825

Now, we try dividing 7,531,825 by 3:

7,531,825 ÷ 3 = 2,510,608.3333

If the quotient is a whole number, then 3 and 2,510,608.3333 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 7,531,825
-1 -7,531,825

Let's try dividing by 4:

7,531,825 ÷ 4 = 1,882,956.25

If the quotient is a whole number, then 4 and 1,882,956.25 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 7,531,825
-1 7,531,825
Keep dividing by the next highest number until you cannot divide anymore.

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

15725351751932239651,1151,3511,5614,8255,5756,7557,80533,77539,02543,039215,195301,2731,075,9751,506,3657,531,825
-1-5-7-25-35-175-193-223-965-1,115-1,351-1,561-4,825-5,575-6,755-7,805-33,775-39,025-43,039-215,195-301,273-1,075,975-1,506,365-7,531,825

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