Q: What are the factor combinations of the number 851,597?

 A:
Positive:   1 x 851597
Negative: -1 x -851597


How do I find the factor combinations of the number 851,597?

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 851,597, 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.

1 851,597
-1 -851,597

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 851,597.

Example:
1 x 851,597 = 851,597
and
-1 x -851,597 = 851,597
Notice both answers equal 851,597

With that explanation out of the way, let's continue. Next, we take the number 851,597 and divide it by 2:

851,597 ÷ 2 = 425,798.5

If the quotient is a whole number, then 2 and 425,798.5 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:

1 851,597
-1 -851,597

Now, we try dividing 851,597 by 3:

851,597 ÷ 3 = 283,865.6667

If the quotient is a whole number, then 3 and 283,865.6667 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:

1 851,597
-1 -851,597

Let's try dividing by 4:

851,597 ÷ 4 = 212,899.25

If the quotient is a whole number, then 4 and 212,899.25 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:

1 851,597
-1 851,597
Keep dividing by the next highest number until you cannot divide anymore.

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

1851,597
-1-851,597

More Examples

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