Q: What are the factor combinations of the number 307,475?

 A:
Positive:   1 x 3074755 x 614957 x 4392525 x 1229935 x 878549 x 6275175 x 1757245 x 1255251 x 1225
Negative: -1 x -307475-5 x -61495-7 x -43925-25 x -12299-35 x -8785-49 x -6275-175 x -1757-245 x -1255-251 x -1225


How do I find the factor combinations of the number 307,475?

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 307,475, 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.

1 307,475
-1 -307,475

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 307,475.

Example:
1 x 307,475 = 307,475
and
-1 x -307,475 = 307,475
Notice both answers equal 307,475

With that explanation out of the way, let's continue. Next, we take the number 307,475 and divide it by 2:

307,475 ÷ 2 = 153,737.5

If the quotient is a whole number, then 2 and 153,737.5 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:

1 307,475
-1 -307,475

Now, we try dividing 307,475 by 3:

307,475 ÷ 3 = 102,491.6667

If the quotient is a whole number, then 3 and 102,491.6667 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:

1 307,475
-1 -307,475

Let's try dividing by 4:

307,475 ÷ 4 = 76,868.75

If the quotient is a whole number, then 4 and 76,868.75 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:

1 307,475
-1 307,475
Keep dividing by the next highest number until you cannot divide anymore.

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

1572535491752452511,2251,2551,7576,2758,78512,29943,92561,495307,475
-1-5-7-25-35-49-175-245-251-1,225-1,255-1,757-6,275-8,785-12,299-43,925-61,495-307,475

More Examples

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