Q: What are the factor combinations of the number 22,124,123?

 A:
Positive:   1 x 221241237 x 316058917 x 1301419119 x 185917
Negative: -1 x -22124123-7 x -3160589-17 x -1301419-119 x -185917


How do I find the factor combinations of the number 22,124,123?

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 22,124,123, 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 22,124,123
-1 -22,124,123

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 22,124,123.

Example:
1 x 22,124,123 = 22,124,123
and
-1 x -22,124,123 = 22,124,123
Notice both answers equal 22,124,123

With that explanation out of the way, let's continue. Next, we take the number 22,124,123 and divide it by 2:

22,124,123 ÷ 2 = 11,062,061.5

If the quotient is a whole number, then 2 and 11,062,061.5 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 22,124,123
-1 -22,124,123

Now, we try dividing 22,124,123 by 3:

22,124,123 ÷ 3 = 7,374,707.6667

If the quotient is a whole number, then 3 and 7,374,707.6667 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 22,124,123
-1 -22,124,123

Let's try dividing by 4:

22,124,123 ÷ 4 = 5,531,030.75

If the quotient is a whole number, then 4 and 5,531,030.75 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 22,124,123
-1 22,124,123
Keep dividing by the next highest number until you cannot divide anymore.

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

1717119185,9171,301,4193,160,58922,124,123
-1-7-17-119-185,917-1,301,419-3,160,589-22,124,123

More Examples

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