Q: What are the factor combinations of the number 1,205,315?

 A:
Positive:   1 x 12053155 x 24106323 x 5240547 x 25645115 x 10481223 x 5405235 x 51291081 x 1115
Negative: -1 x -1205315-5 x -241063-23 x -52405-47 x -25645-115 x -10481-223 x -5405-235 x -5129-1081 x -1115


How do I find the factor combinations of the number 1,205,315?

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 1,205,315, 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 1,205,315
-1 -1,205,315

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 1,205,315.

Example:
1 x 1,205,315 = 1,205,315
and
-1 x -1,205,315 = 1,205,315
Notice both answers equal 1,205,315

With that explanation out of the way, let's continue. Next, we take the number 1,205,315 and divide it by 2:

1,205,315 ÷ 2 = 602,657.5

If the quotient is a whole number, then 2 and 602,657.5 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 1,205,315
-1 -1,205,315

Now, we try dividing 1,205,315 by 3:

1,205,315 ÷ 3 = 401,771.6667

If the quotient is a whole number, then 3 and 401,771.6667 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 1,205,315
-1 -1,205,315

Let's try dividing by 4:

1,205,315 ÷ 4 = 301,328.75

If the quotient is a whole number, then 4 and 301,328.75 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 1,205,315
-1 1,205,315
Keep dividing by the next highest number until you cannot divide anymore.

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

1523471152232351,0811,1155,1295,40510,48125,64552,405241,0631,205,315
-1-5-23-47-115-223-235-1,081-1,115-5,129-5,405-10,481-25,645-52,405-241,063-1,205,315

More Examples

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