Q: What are the factor combinations of the number 120,454,213?

 A:
Positive:   1 x 12045421311 x 1095038353 x 2272721307 x 392359583 x 206611673 x 1789813377 x 356697403 x 16271
Negative: -1 x -120454213-11 x -10950383-53 x -2272721-307 x -392359-583 x -206611-673 x -178981-3377 x -35669-7403 x -16271


How do I find the factor combinations of the number 120,454,213?

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 120,454,213, 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.

1 120,454,213
-1 -120,454,213

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 120,454,213.

Example:
1 x 120,454,213 = 120,454,213
and
-1 x -120,454,213 = 120,454,213
Notice both answers equal 120,454,213

With that explanation out of the way, let's continue. Next, we take the number 120,454,213 and divide it by 2:

120,454,213 ÷ 2 = 60,227,106.5

If the quotient is a whole number, then 2 and 60,227,106.5 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:

1 120,454,213
-1 -120,454,213

Now, we try dividing 120,454,213 by 3:

120,454,213 ÷ 3 = 40,151,404.3333

If the quotient is a whole number, then 3 and 40,151,404.3333 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:

1 120,454,213
-1 -120,454,213

Let's try dividing by 4:

120,454,213 ÷ 4 = 30,113,553.25

If the quotient is a whole number, then 4 and 30,113,553.25 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:

1 120,454,213
-1 120,454,213
Keep dividing by the next highest number until you cannot divide anymore.

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

111533075836733,3777,40316,27135,669178,981206,611392,3592,272,72110,950,383120,454,213
-1-11-53-307-583-673-3,377-7,403-16,271-35,669-178,981-206,611-392,359-2,272,721-10,950,383-120,454,213

More Examples

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