Q: What are the factor combinations of the number 238,525?

 A:
Positive:   1 x 2385255 x 477057 x 3407525 x 954129 x 822535 x 681547 x 5075145 x 1645175 x 1363203 x 1175235 x 1015329 x 725
Negative: -1 x -238525-5 x -47705-7 x -34075-25 x -9541-29 x -8225-35 x -6815-47 x -5075-145 x -1645-175 x -1363-203 x -1175-235 x -1015-329 x -725


How do I find the factor combinations of the number 238,525?

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 238,525, 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.

1 238,525
-1 -238,525

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 238,525.

Example:
1 x 238,525 = 238,525
and
-1 x -238,525 = 238,525
Notice both answers equal 238,525

With that explanation out of the way, let's continue. Next, we take the number 238,525 and divide it by 2:

238,525 ÷ 2 = 119,262.5

If the quotient is a whole number, then 2 and 119,262.5 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:

1 238,525
-1 -238,525

Now, we try dividing 238,525 by 3:

238,525 ÷ 3 = 79,508.3333

If the quotient is a whole number, then 3 and 79,508.3333 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:

1 238,525
-1 -238,525

Let's try dividing by 4:

238,525 ÷ 4 = 59,631.25

If the quotient is a whole number, then 4 and 59,631.25 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:

1 238,525
-1 238,525
Keep dividing by the next highest number until you cannot divide anymore.

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

157252935471451752032353297251,0151,1751,3631,6455,0756,8158,2259,54134,07547,705238,525
-1-5-7-25-29-35-47-145-175-203-235-329-725-1,015-1,175-1,363-1,645-5,075-6,815-8,225-9,541-34,075-47,705-238,525

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