Q: What are the factor combinations of the number 67,675?

 A:
Positive:   1 x 676755 x 1353525 x 2707
Negative: -1 x -67675-5 x -13535-25 x -2707


How do I find the factor combinations of the number 67,675?

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 67,675, 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 67,675
-1 -67,675

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 67,675.

Example:
1 x 67,675 = 67,675
and
-1 x -67,675 = 67,675
Notice both answers equal 67,675

With that explanation out of the way, let's continue. Next, we take the number 67,675 and divide it by 2:

67,675 ÷ 2 = 33,837.5

If the quotient is a whole number, then 2 and 33,837.5 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 67,675
-1 -67,675

Now, we try dividing 67,675 by 3:

67,675 ÷ 3 = 22,558.3333

If the quotient is a whole number, then 3 and 22,558.3333 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 67,675
-1 -67,675

Let's try dividing by 4:

67,675 ÷ 4 = 16,918.75

If the quotient is a whole number, then 4 and 16,918.75 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 67,675
-1 67,675
Keep dividing by the next highest number until you cannot divide anymore.

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

15252,70713,53567,675
-1-5-25-2,707-13,535-67,675

More Examples

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