Q: What are the factor combinations of the number 307,515,725?

 A:
Positive:   1 x 3075157255 x 6150314511 x 2795597525 x 1230062955 x 5591195275 x 1118239751 x 4094751489 x 2065253755 x 818957445 x 413058261 x 3722516379 x 18775
Negative: -1 x -307515725-5 x -61503145-11 x -27955975-25 x -12300629-55 x -5591195-275 x -1118239-751 x -409475-1489 x -206525-3755 x -81895-7445 x -41305-8261 x -37225-16379 x -18775


How do I find the factor combinations of the number 307,515,725?

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 307,515,725, 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.

1 307,515,725
-1 -307,515,725

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 307,515,725.

Example:
1 x 307,515,725 = 307,515,725
and
-1 x -307,515,725 = 307,515,725
Notice both answers equal 307,515,725

With that explanation out of the way, let's continue. Next, we take the number 307,515,725 and divide it by 2:

307,515,725 ÷ 2 = 153,757,862.5

If the quotient is a whole number, then 2 and 153,757,862.5 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:

1 307,515,725
-1 -307,515,725

Now, we try dividing 307,515,725 by 3:

307,515,725 ÷ 3 = 102,505,241.6667

If the quotient is a whole number, then 3 and 102,505,241.6667 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:

1 307,515,725
-1 -307,515,725

Let's try dividing by 4:

307,515,725 ÷ 4 = 76,878,931.25

If the quotient is a whole number, then 4 and 76,878,931.25 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:

1 307,515,725
-1 307,515,725
Keep dividing by the next highest number until you cannot divide anymore.

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

151125552757511,4893,7557,4458,26116,37918,77537,22541,30581,895206,525409,4751,118,2395,591,19512,300,62927,955,97561,503,145307,515,725
-1-5-11-25-55-275-751-1,489-3,755-7,445-8,261-16,379-18,775-37,225-41,305-81,895-206,525-409,475-1,118,239-5,591,195-12,300,629-27,955,975-61,503,145-307,515,725

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