Q: What are the factor combinations of the number 431,375?

 A:
Positive:   1 x 4313755 x 862757 x 6162517 x 2537525 x 1725529 x 1487535 x 1232585 x 5075119 x 3625125 x 3451145 x 2975175 x 2465203 x 2125425 x 1015493 x 875595 x 725
Negative: -1 x -431375-5 x -86275-7 x -61625-17 x -25375-25 x -17255-29 x -14875-35 x -12325-85 x -5075-119 x -3625-125 x -3451-145 x -2975-175 x -2465-203 x -2125-425 x -1015-493 x -875-595 x -725


How do I find the factor combinations of the number 431,375?

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 431,375, 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.

1 431,375
-1 -431,375

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 431,375.

Example:
1 x 431,375 = 431,375
and
-1 x -431,375 = 431,375
Notice both answers equal 431,375

With that explanation out of the way, let's continue. Next, we take the number 431,375 and divide it by 2:

431,375 ÷ 2 = 215,687.5

If the quotient is a whole number, then 2 and 215,687.5 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:

1 431,375
-1 -431,375

Now, we try dividing 431,375 by 3:

431,375 ÷ 3 = 143,791.6667

If the quotient is a whole number, then 3 and 143,791.6667 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:

1 431,375
-1 -431,375

Let's try dividing by 4:

431,375 ÷ 4 = 107,843.75

If the quotient is a whole number, then 4 and 107,843.75 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:

1 431,375
-1 431,375
Keep dividing by the next highest number until you cannot divide anymore.

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

15717252935851191251451752034254935957258751,0152,1252,4652,9753,4513,6255,07512,32514,87517,25525,37561,62586,275431,375
-1-5-7-17-25-29-35-85-119-125-145-175-203-425-493-595-725-875-1,015-2,125-2,465-2,975-3,451-3,625-5,075-12,325-14,875-17,255-25,375-61,625-86,275-431,375

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