Q: What are the factor combinations of the number 671,371?

 A:
Positive:   1 x 671371509 x 1319
Negative: -1 x -671371-509 x -1319


How do I find the factor combinations of the number 671,371?

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 671,371, 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.

1 671,371
-1 -671,371

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 671,371.

Example:
1 x 671,371 = 671,371
and
-1 x -671,371 = 671,371
Notice both answers equal 671,371

With that explanation out of the way, let's continue. Next, we take the number 671,371 and divide it by 2:

671,371 ÷ 2 = 335,685.5

If the quotient is a whole number, then 2 and 335,685.5 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:

1 671,371
-1 -671,371

Now, we try dividing 671,371 by 3:

671,371 ÷ 3 = 223,790.3333

If the quotient is a whole number, then 3 and 223,790.3333 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:

1 671,371
-1 -671,371

Let's try dividing by 4:

671,371 ÷ 4 = 167,842.75

If the quotient is a whole number, then 4 and 167,842.75 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:

1 671,371
-1 671,371
Keep dividing by the next highest number until you cannot divide anymore.

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

15091,319671,371
-1-509-1,319-671,371

More Examples

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