Q: What are the factor combinations of the number 306,375,275?

 A:
Positive:   1 x 3063752755 x 6127505517 x 1802207525 x 1225501185 x 3604415263 x 1164925425 x 7208831315 x 2329852741 x 1117754471 x 685256575 x 4659713705 x 22355
Negative: -1 x -306375275-5 x -61275055-17 x -18022075-25 x -12255011-85 x -3604415-263 x -1164925-425 x -720883-1315 x -232985-2741 x -111775-4471 x -68525-6575 x -46597-13705 x -22355


How do I find the factor combinations of the number 306,375,275?

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 306,375,275, 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.

1 306,375,275
-1 -306,375,275

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 306,375,275.

Example:
1 x 306,375,275 = 306,375,275
and
-1 x -306,375,275 = 306,375,275
Notice both answers equal 306,375,275

With that explanation out of the way, let's continue. Next, we take the number 306,375,275 and divide it by 2:

306,375,275 ÷ 2 = 153,187,637.5

If the quotient is a whole number, then 2 and 153,187,637.5 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:

1 306,375,275
-1 -306,375,275

Now, we try dividing 306,375,275 by 3:

306,375,275 ÷ 3 = 102,125,091.6667

If the quotient is a whole number, then 3 and 102,125,091.6667 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:

1 306,375,275
-1 -306,375,275

Let's try dividing by 4:

306,375,275 ÷ 4 = 76,593,818.75

If the quotient is a whole number, then 4 and 76,593,818.75 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:

1 306,375,275
-1 306,375,275
Keep dividing by the next highest number until you cannot divide anymore.

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

151725852634251,3152,7414,4716,57513,70522,35546,59768,525111,775232,985720,8831,164,9253,604,41512,255,01118,022,07561,275,055306,375,275
-1-5-17-25-85-263-425-1,315-2,741-4,471-6,575-13,705-22,355-46,597-68,525-111,775-232,985-720,883-1,164,925-3,604,415-12,255,011-18,022,075-61,275,055-306,375,275

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