Q: What are the factor combinations of the number 7,535,825?

 A:
Positive:   1 x 75358255 x 150716511 x 68507525 x 30143355 x 13701567 x 112475275 x 27403335 x 22495409 x 18425737 x 102251675 x 44992045 x 3685
Negative: -1 x -7535825-5 x -1507165-11 x -685075-25 x -301433-55 x -137015-67 x -112475-275 x -27403-335 x -22495-409 x -18425-737 x -10225-1675 x -4499-2045 x -3685


How do I find the factor combinations of the number 7,535,825?

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 7,535,825, 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 7,535,825
-1 -7,535,825

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 7,535,825.

Example:
1 x 7,535,825 = 7,535,825
and
-1 x -7,535,825 = 7,535,825
Notice both answers equal 7,535,825

With that explanation out of the way, let's continue. Next, we take the number 7,535,825 and divide it by 2:

7,535,825 ÷ 2 = 3,767,912.5

If the quotient is a whole number, then 2 and 3,767,912.5 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 7,535,825
-1 -7,535,825

Now, we try dividing 7,535,825 by 3:

7,535,825 ÷ 3 = 2,511,941.6667

If the quotient is a whole number, then 3 and 2,511,941.6667 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 7,535,825
-1 -7,535,825

Let's try dividing by 4:

7,535,825 ÷ 4 = 1,883,956.25

If the quotient is a whole number, then 4 and 1,883,956.25 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 7,535,825
-1 7,535,825
Keep dividing by the next highest number until you cannot divide anymore.

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

15112555672753354097371,6752,0453,6854,49910,22518,42522,49527,403112,475137,015301,433685,0751,507,1657,535,825
-1-5-11-25-55-67-275-335-409-737-1,675-2,045-3,685-4,499-10,225-18,425-22,495-27,403-112,475-137,015-301,433-685,075-1,507,165-7,535,825

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