Q: What are the factor combinations of the number 3,212,315?

 A:
Positive:   1 x 32123155 x 64246343 x 7470567 x 47945215 x 14941223 x 14405335 x 95891115 x 2881
Negative: -1 x -3212315-5 x -642463-43 x -74705-67 x -47945-215 x -14941-223 x -14405-335 x -9589-1115 x -2881


How do I find the factor combinations of the number 3,212,315?

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 3,212,315, 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 3,212,315
-1 -3,212,315

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 3,212,315.

Example:
1 x 3,212,315 = 3,212,315
and
-1 x -3,212,315 = 3,212,315
Notice both answers equal 3,212,315

With that explanation out of the way, let's continue. Next, we take the number 3,212,315 and divide it by 2:

3,212,315 ÷ 2 = 1,606,157.5

If the quotient is a whole number, then 2 and 1,606,157.5 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 3,212,315
-1 -3,212,315

Now, we try dividing 3,212,315 by 3:

3,212,315 ÷ 3 = 1,070,771.6667

If the quotient is a whole number, then 3 and 1,070,771.6667 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 3,212,315
-1 -3,212,315

Let's try dividing by 4:

3,212,315 ÷ 4 = 803,078.75

If the quotient is a whole number, then 4 and 803,078.75 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 3,212,315
-1 3,212,315
Keep dividing by the next highest number until you cannot divide anymore.

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

1543672152233351,1152,8819,58914,40514,94147,94574,705642,4633,212,315
-1-5-43-67-215-223-335-1,115-2,881-9,589-14,405-14,941-47,945-74,705-642,463-3,212,315

More Examples

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