Q: What are the factor combinations of the number 12,145,123?

 A:
Positive:   1 x 1214512317 x 71441919 x 639217323 x 37601361 x 336431979 x 6137
Negative: -1 x -12145123-17 x -714419-19 x -639217-323 x -37601-361 x -33643-1979 x -6137


How do I find the factor combinations of the number 12,145,123?

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 12,145,123, 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 12,145,123
-1 -12,145,123

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 12,145,123.

Example:
1 x 12,145,123 = 12,145,123
and
-1 x -12,145,123 = 12,145,123
Notice both answers equal 12,145,123

With that explanation out of the way, let's continue. Next, we take the number 12,145,123 and divide it by 2:

12,145,123 ÷ 2 = 6,072,561.5

If the quotient is a whole number, then 2 and 6,072,561.5 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 12,145,123
-1 -12,145,123

Now, we try dividing 12,145,123 by 3:

12,145,123 ÷ 3 = 4,048,374.3333

If the quotient is a whole number, then 3 and 4,048,374.3333 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 12,145,123
-1 -12,145,123

Let's try dividing by 4:

12,145,123 ÷ 4 = 3,036,280.75

If the quotient is a whole number, then 4 and 3,036,280.75 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 12,145,123
-1 12,145,123
Keep dividing by the next highest number until you cannot divide anymore.

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

117193233611,9796,13733,64337,601639,217714,41912,145,123
-1-17-19-323-361-1,979-6,137-33,643-37,601-639,217-714,419-12,145,123

More Examples

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