Q: What are the factor combinations of the number 700,825?

 A:
Positive:   1 x 7008255 x 14016517 x 4122525 x 2803385 x 824597 x 7225289 x 2425425 x 1649485 x 1445
Negative: -1 x -700825-5 x -140165-17 x -41225-25 x -28033-85 x -8245-97 x -7225-289 x -2425-425 x -1649-485 x -1445


How do I find the factor combinations of the number 700,825?

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 700,825, 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.

1 700,825
-1 -700,825

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 700,825.

Example:
1 x 700,825 = 700,825
and
-1 x -700,825 = 700,825
Notice both answers equal 700,825

With that explanation out of the way, let's continue. Next, we take the number 700,825 and divide it by 2:

700,825 ÷ 2 = 350,412.5

If the quotient is a whole number, then 2 and 350,412.5 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:

1 700,825
-1 -700,825

Now, we try dividing 700,825 by 3:

700,825 ÷ 3 = 233,608.3333

If the quotient is a whole number, then 3 and 233,608.3333 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:

1 700,825
-1 -700,825

Let's try dividing by 4:

700,825 ÷ 4 = 175,206.25

If the quotient is a whole number, then 4 and 175,206.25 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:

1 700,825
-1 700,825
Keep dividing by the next highest number until you cannot divide anymore.

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

15172585972894254851,4451,6492,4257,2258,24528,03341,225140,165700,825
-1-5-17-25-85-97-289-425-485-1,445-1,649-2,425-7,225-8,245-28,033-41,225-140,165-700,825

More Examples

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