Q: What are the factor combinations of the number 338,975?

 A:
Positive:   1 x 3389755 x 677957 x 4842513 x 2607525 x 1355935 x 968565 x 521591 x 3725149 x 2275175 x 1937325 x 1043455 x 745
Negative: -1 x -338975-5 x -67795-7 x -48425-13 x -26075-25 x -13559-35 x -9685-65 x -5215-91 x -3725-149 x -2275-175 x -1937-325 x -1043-455 x -745


How do I find the factor combinations of the number 338,975?

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 338,975, 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.

1 338,975
-1 -338,975

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 338,975.

Example:
1 x 338,975 = 338,975
and
-1 x -338,975 = 338,975
Notice both answers equal 338,975

With that explanation out of the way, let's continue. Next, we take the number 338,975 and divide it by 2:

338,975 ÷ 2 = 169,487.5

If the quotient is a whole number, then 2 and 169,487.5 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:

1 338,975
-1 -338,975

Now, we try dividing 338,975 by 3:

338,975 ÷ 3 = 112,991.6667

If the quotient is a whole number, then 3 and 112,991.6667 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:

1 338,975
-1 -338,975

Let's try dividing by 4:

338,975 ÷ 4 = 84,743.75

If the quotient is a whole number, then 4 and 84,743.75 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:

1 338,975
-1 338,975
Keep dividing by the next highest number until you cannot divide anymore.

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

15713253565911491753254557451,0431,9372,2753,7255,2159,68513,55926,07548,42567,795338,975
-1-5-7-13-25-35-65-91-149-175-325-455-745-1,043-1,937-2,275-3,725-5,215-9,685-13,559-26,075-48,425-67,795-338,975

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