Q: What are the factor combinations of the number 312,221?

How do I find the factor combinations of the number 312,221?

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 312,221, 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		312,221
-1		-312,221

With that explanation out of the way, let's continue. Next, we take the number 312,221 and divide it by 2:

312,221 ÷ 2 = 156,110.5

If the quotient is a whole number, then 2 and 156,110.5 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:

Now, we try dividing 312,221 by 3:

312,221 ÷ 3 = 104,073.6667

If the quotient is a whole number, then 3 and 104,073.6667 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:

Let's try dividing by 4:

312,221 ÷ 4 = 78,055.25

If the quotient is a whole number, then 4 and 78,055.25 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:

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

More Examples

Here are some more numbers to try:

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