Q: What are the factor combinations of the number 304,285,225?

 A:
Positive:   1 x 3042852255 x 6085704525 x 1217140937 x 8223925101 x 3012725185 x 1644785505 x 602545925 x 3289572525 x 1205093257 x 934253737 x 8142516285 x 18685
Negative: -1 x -304285225-5 x -60857045-25 x -12171409-37 x -8223925-101 x -3012725-185 x -1644785-505 x -602545-925 x -328957-2525 x -120509-3257 x -93425-3737 x -81425-16285 x -18685


How do I find the factor combinations of the number 304,285,225?

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 304,285,225, 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.

1 304,285,225
-1 -304,285,225

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 304,285,225.

Example:
1 x 304,285,225 = 304,285,225
and
-1 x -304,285,225 = 304,285,225
Notice both answers equal 304,285,225

With that explanation out of the way, let's continue. Next, we take the number 304,285,225 and divide it by 2:

304,285,225 ÷ 2 = 152,142,612.5

If the quotient is a whole number, then 2 and 152,142,612.5 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:

1 304,285,225
-1 -304,285,225

Now, we try dividing 304,285,225 by 3:

304,285,225 ÷ 3 = 101,428,408.3333

If the quotient is a whole number, then 3 and 101,428,408.3333 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:

1 304,285,225
-1 -304,285,225

Let's try dividing by 4:

304,285,225 ÷ 4 = 76,071,306.25

If the quotient is a whole number, then 4 and 76,071,306.25 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:

1 304,285,225
-1 304,285,225
Keep dividing by the next highest number until you cannot divide anymore.

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

1525371011855059252,5253,2573,73716,28518,68581,42593,425120,509328,957602,5451,644,7853,012,7258,223,92512,171,40960,857,045304,285,225
-1-5-25-37-101-185-505-925-2,525-3,257-3,737-16,285-18,685-81,425-93,425-120,509-328,957-602,545-1,644,785-3,012,725-8,223,925-12,171,409-60,857,045-304,285,225

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