Q: What are the factor combinations of the number 304,310,875?

 A:
Positive:   1 x 3043108755 x 6086217511 x 2766462525 x 1217243555 x 5532925125 x 2434487275 x 11065851375 x 221317
Negative: -1 x -304310875-5 x -60862175-11 x -27664625-25 x -12172435-55 x -5532925-125 x -2434487-275 x -1106585-1375 x -221317


How do I find the factor combinations of the number 304,310,875?

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 304,310,875, 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.

1 304,310,875
-1 -304,310,875

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 304,310,875.

Example:
1 x 304,310,875 = 304,310,875
and
-1 x -304,310,875 = 304,310,875
Notice both answers equal 304,310,875

With that explanation out of the way, let's continue. Next, we take the number 304,310,875 and divide it by 2:

304,310,875 ÷ 2 = 152,155,437.5

If the quotient is a whole number, then 2 and 152,155,437.5 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:

1 304,310,875
-1 -304,310,875

Now, we try dividing 304,310,875 by 3:

304,310,875 ÷ 3 = 101,436,958.3333

If the quotient is a whole number, then 3 and 101,436,958.3333 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:

1 304,310,875
-1 -304,310,875

Let's try dividing by 4:

304,310,875 ÷ 4 = 76,077,718.75

If the quotient is a whole number, then 4 and 76,077,718.75 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:

1 304,310,875
-1 304,310,875
Keep dividing by the next highest number until you cannot divide anymore.

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

151125551252751,375221,3171,106,5852,434,4875,532,92512,172,43527,664,62560,862,175304,310,875
-1-5-11-25-55-125-275-1,375-221,317-1,106,585-2,434,487-5,532,925-12,172,435-27,664,625-60,862,175-304,310,875

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