Q: What are the factor combinations of the number 638,825?

 A:
Positive:   1 x 6388255 x 12776511 x 5807523 x 2777525 x 2555355 x 11615101 x 6325115 x 5555253 x 2525275 x 2323505 x 1265575 x 1111
Negative: -1 x -638825-5 x -127765-11 x -58075-23 x -27775-25 x -25553-55 x -11615-101 x -6325-115 x -5555-253 x -2525-275 x -2323-505 x -1265-575 x -1111


How do I find the factor combinations of the number 638,825?

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 638,825, 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.

1 638,825
-1 -638,825

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 638,825.

Example:
1 x 638,825 = 638,825
and
-1 x -638,825 = 638,825
Notice both answers equal 638,825

With that explanation out of the way, let's continue. Next, we take the number 638,825 and divide it by 2:

638,825 ÷ 2 = 319,412.5

If the quotient is a whole number, then 2 and 319,412.5 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:

1 638,825
-1 -638,825

Now, we try dividing 638,825 by 3:

638,825 ÷ 3 = 212,941.6667

If the quotient is a whole number, then 3 and 212,941.6667 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:

1 638,825
-1 -638,825

Let's try dividing by 4:

638,825 ÷ 4 = 159,706.25

If the quotient is a whole number, then 4 and 159,706.25 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:

1 638,825
-1 638,825
Keep dividing by the next highest number until you cannot divide anymore.

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

15112325551011152532755055751,1111,2652,3232,5255,5556,32511,61525,55327,77558,075127,765638,825
-1-5-11-23-25-55-101-115-253-275-505-575-1,111-1,265-2,323-2,525-5,555-6,325-11,615-25,553-27,775-58,075-127,765-638,825

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