Q: What are the factor combinations of the number 638,575?

 A:
Positive:   1 x 6385755 x 1277157 x 9122525 x 2554335 x 1824541 x 1557589 x 7175175 x 3649205 x 3115287 x 2225445 x 1435623 x 1025
Negative: -1 x -638575-5 x -127715-7 x -91225-25 x -25543-35 x -18245-41 x -15575-89 x -7175-175 x -3649-205 x -3115-287 x -2225-445 x -1435-623 x -1025


How do I find the factor combinations of the number 638,575?

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 638,575, 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.

1 638,575
-1 -638,575

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 638,575.

Example:
1 x 638,575 = 638,575
and
-1 x -638,575 = 638,575
Notice both answers equal 638,575

With that explanation out of the way, let's continue. Next, we take the number 638,575 and divide it by 2:

638,575 ÷ 2 = 319,287.5

If the quotient is a whole number, then 2 and 319,287.5 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:

1 638,575
-1 -638,575

Now, we try dividing 638,575 by 3:

638,575 ÷ 3 = 212,858.3333

If the quotient is a whole number, then 3 and 212,858.3333 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:

1 638,575
-1 -638,575

Let's try dividing by 4:

638,575 ÷ 4 = 159,643.75

If the quotient is a whole number, then 4 and 159,643.75 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:

1 638,575
-1 638,575
Keep dividing by the next highest number until you cannot divide anymore.

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

157253541891752052874456231,0251,4352,2253,1153,6497,17515,57518,24525,54391,225127,715638,575
-1-5-7-25-35-41-89-175-205-287-445-623-1,025-1,435-2,225-3,115-3,649-7,175-15,575-18,245-25,543-91,225-127,715-638,575

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