Q: What are the factor combinations of the number 302,210,315?

 A:
Positive:   1 x 3022103155 x 6044206311 x 2747366555 x 5494733571 x 5292652855 x 1058536281 x 481159623 x 31405
Negative: -1 x -302210315-5 x -60442063-11 x -27473665-55 x -5494733-571 x -529265-2855 x -105853-6281 x -48115-9623 x -31405


How do I find the factor combinations of the number 302,210,315?

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 302,210,315, 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.

1 302,210,315
-1 -302,210,315

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 302,210,315.

Example:
1 x 302,210,315 = 302,210,315
and
-1 x -302,210,315 = 302,210,315
Notice both answers equal 302,210,315

With that explanation out of the way, let's continue. Next, we take the number 302,210,315 and divide it by 2:

302,210,315 ÷ 2 = 151,105,157.5

If the quotient is a whole number, then 2 and 151,105,157.5 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:

1 302,210,315
-1 -302,210,315

Now, we try dividing 302,210,315 by 3:

302,210,315 ÷ 3 = 100,736,771.6667

If the quotient is a whole number, then 3 and 100,736,771.6667 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:

1 302,210,315
-1 -302,210,315

Let's try dividing by 4:

302,210,315 ÷ 4 = 75,552,578.75

If the quotient is a whole number, then 4 and 75,552,578.75 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:

1 302,210,315
-1 302,210,315
Keep dividing by the next highest number until you cannot divide anymore.

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

1511555712,8556,2819,62331,40548,115105,853529,2655,494,73327,473,66560,442,063302,210,315
-1-5-11-55-571-2,855-6,281-9,623-31,405-48,115-105,853-529,265-5,494,733-27,473,665-60,442,063-302,210,315

More Examples

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