Q: What are the factor combinations of the number 625,912?

 A:
Positive:   1 x 6259122 x 3129564 x 1564787 x 894168 x 7823914 x 4470828 x 2235456 x 11177
Negative: -1 x -625912-2 x -312956-4 x -156478-7 x -89416-8 x -78239-14 x -44708-28 x -22354-56 x -11177


How do I find the factor combinations of the number 625,912?

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 625,912, 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.

1 625,912
-1 -625,912

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 625,912.

Example:
1 x 625,912 = 625,912
and
-1 x -625,912 = 625,912
Notice both answers equal 625,912

With that explanation out of the way, let's continue. Next, we take the number 625,912 and divide it by 2:

625,912 ÷ 2 = 312,956

If the quotient is a whole number, then 2 and 312,956 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 312,956 625,912
-1 -2 -312,956 -625,912

Now, we try dividing 625,912 by 3:

625,912 ÷ 3 = 208,637.3333

If the quotient is a whole number, then 3 and 208,637.3333 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 2 312,956 625,912
-1 -2 -312,956 -625,912

Let's try dividing by 4:

625,912 ÷ 4 = 156,478

If the quotient is a whole number, then 4 and 156,478 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 4 156,478 312,956 625,912
-1 -2 -4 -156,478 -312,956 625,912
Keep dividing by the next highest number until you cannot divide anymore.

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

1247814285611,17722,35444,70878,23989,416156,478312,956625,912
-1-2-4-7-8-14-28-56-11,177-22,354-44,708-78,239-89,416-156,478-312,956-625,912

More Examples

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