Q: What are the factor combinations of the number 132,419?

 A:
Positive:   1 x 1324197 x 18917
Negative: -1 x -132419-7 x -18917


How do I find the factor combinations of the number 132,419?

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 132,419, 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.

1 132,419
-1 -132,419

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 132,419.

Example:
1 x 132,419 = 132,419
and
-1 x -132,419 = 132,419
Notice both answers equal 132,419

With that explanation out of the way, let's continue. Next, we take the number 132,419 and divide it by 2:

132,419 ÷ 2 = 66,209.5

If the quotient is a whole number, then 2 and 66,209.5 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:

1 132,419
-1 -132,419

Now, we try dividing 132,419 by 3:

132,419 ÷ 3 = 44,139.6667

If the quotient is a whole number, then 3 and 44,139.6667 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:

1 132,419
-1 -132,419

Let's try dividing by 4:

132,419 ÷ 4 = 33,104.75

If the quotient is a whole number, then 4 and 33,104.75 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:

1 132,419
-1 132,419
Keep dividing by the next highest number until you cannot divide anymore.

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

1718,917132,419
-1-7-18,917-132,419

More Examples

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