Q: What are the factor combinations of the number 317,975?

 A:
Positive:   1 x 3179755 x 635957 x 4542523 x 1382525 x 1271935 x 908579 x 4025115 x 2765161 x 1975175 x 1817395 x 805553 x 575
Negative: -1 x -317975-5 x -63595-7 x -45425-23 x -13825-25 x -12719-35 x -9085-79 x -4025-115 x -2765-161 x -1975-175 x -1817-395 x -805-553 x -575


How do I find the factor combinations of the number 317,975?

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 317,975, 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.

1 317,975
-1 -317,975

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 317,975.

Example:
1 x 317,975 = 317,975
and
-1 x -317,975 = 317,975
Notice both answers equal 317,975

With that explanation out of the way, let's continue. Next, we take the number 317,975 and divide it by 2:

317,975 ÷ 2 = 158,987.5

If the quotient is a whole number, then 2 and 158,987.5 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:

1 317,975
-1 -317,975

Now, we try dividing 317,975 by 3:

317,975 ÷ 3 = 105,991.6667

If the quotient is a whole number, then 3 and 105,991.6667 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:

1 317,975
-1 -317,975

Let's try dividing by 4:

317,975 ÷ 4 = 79,493.75

If the quotient is a whole number, then 4 and 79,493.75 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:

1 317,975
-1 317,975
Keep dividing by the next highest number until you cannot divide anymore.

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

157232535791151611753955535758051,8171,9752,7654,0259,08512,71913,82545,42563,595317,975
-1-5-7-23-25-35-79-115-161-175-395-553-575-805-1,817-1,975-2,765-4,025-9,085-12,719-13,825-45,425-63,595-317,975

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