Q: What are the factor combinations of the number 204,121?

 A:
Positive:   1 x 20412143 x 474747 x 4343101 x 2021
Negative: -1 x -204121-43 x -4747-47 x -4343-101 x -2021


How do I find the factor combinations of the number 204,121?

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 204,121, 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.

1 204,121
-1 -204,121

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 204,121.

Example:
1 x 204,121 = 204,121
and
-1 x -204,121 = 204,121
Notice both answers equal 204,121

With that explanation out of the way, let's continue. Next, we take the number 204,121 and divide it by 2:

204,121 ÷ 2 = 102,060.5

If the quotient is a whole number, then 2 and 102,060.5 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:

1 204,121
-1 -204,121

Now, we try dividing 204,121 by 3:

204,121 ÷ 3 = 68,040.3333

If the quotient is a whole number, then 3 and 68,040.3333 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:

1 204,121
-1 -204,121

Let's try dividing by 4:

204,121 ÷ 4 = 51,030.25

If the quotient is a whole number, then 4 and 51,030.25 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:

1 204,121
-1 204,121
Keep dividing by the next highest number until you cannot divide anymore.

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

143471012,0214,3434,747204,121
-1-43-47-101-2,021-4,343-4,747-204,121

More Examples

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