Q: What are the factor combinations of the number 310,204,013?

 A:
Positive:   1 x 3102040137 x 4431485919 x 1632652723 x 13487131133 x 2332361161 x 1926733437 x 709849529 x 5863973059 x 1014073703 x 837714409 x 7035710051 x 30863
Negative: -1 x -310204013-7 x -44314859-19 x -16326527-23 x -13487131-133 x -2332361-161 x -1926733-437 x -709849-529 x -586397-3059 x -101407-3703 x -83771-4409 x -70357-10051 x -30863


How do I find the factor combinations of the number 310,204,013?

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 310,204,013, 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.

1 310,204,013
-1 -310,204,013

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 310,204,013.

Example:
1 x 310,204,013 = 310,204,013
and
-1 x -310,204,013 = 310,204,013
Notice both answers equal 310,204,013

With that explanation out of the way, let's continue. Next, we take the number 310,204,013 and divide it by 2:

310,204,013 ÷ 2 = 155,102,006.5

If the quotient is a whole number, then 2 and 155,102,006.5 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:

1 310,204,013
-1 -310,204,013

Now, we try dividing 310,204,013 by 3:

310,204,013 ÷ 3 = 103,401,337.6667

If the quotient is a whole number, then 3 and 103,401,337.6667 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:

1 310,204,013
-1 -310,204,013

Let's try dividing by 4:

310,204,013 ÷ 4 = 77,551,003.25

If the quotient is a whole number, then 4 and 77,551,003.25 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:

1 310,204,013
-1 310,204,013
Keep dividing by the next highest number until you cannot divide anymore.

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

1719231331614375293,0593,7034,40910,05130,86370,35783,771101,407586,397709,8491,926,7332,332,36113,487,13116,326,52744,314,859310,204,013
-1-7-19-23-133-161-437-529-3,059-3,703-4,409-10,051-30,863-70,357-83,771-101,407-586,397-709,849-1,926,733-2,332,361-13,487,131-16,326,527-44,314,859-310,204,013

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