Q: What are the factor combinations of the number 294,221?

 A:
Positive:   1 x 29422131 x 9491
Negative: -1 x -294221-31 x -9491


How do I find the factor combinations of the number 294,221?

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 294,221, 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.

1 294,221
-1 -294,221

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 294,221.

Example:
1 x 294,221 = 294,221
and
-1 x -294,221 = 294,221
Notice both answers equal 294,221

With that explanation out of the way, let's continue. Next, we take the number 294,221 and divide it by 2:

294,221 ÷ 2 = 147,110.5

If the quotient is a whole number, then 2 and 147,110.5 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:

1 294,221
-1 -294,221

Now, we try dividing 294,221 by 3:

294,221 ÷ 3 = 98,073.6667

If the quotient is a whole number, then 3 and 98,073.6667 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:

1 294,221
-1 -294,221

Let's try dividing by 4:

294,221 ÷ 4 = 73,555.25

If the quotient is a whole number, then 4 and 73,555.25 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:

1 294,221
-1 294,221
Keep dividing by the next highest number until you cannot divide anymore.

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

1319,491294,221
-1-31-9,491-294,221

More Examples

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