Q: What are the factor combinations of the number 23,422,345?

 A:
Positive:   1 x 234223455 x 468446917 x 137778519 x 123275585 x 27555795 x 246551323 x 725151615 x 14503
Negative: -1 x -23422345-5 x -4684469-17 x -1377785-19 x -1232755-85 x -275557-95 x -246551-323 x -72515-1615 x -14503


How do I find the factor combinations of the number 23,422,345?

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 23,422,345, 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 23,422,345
-1 -23,422,345

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 23,422,345.

Example:
1 x 23,422,345 = 23,422,345
and
-1 x -23,422,345 = 23,422,345
Notice both answers equal 23,422,345

With that explanation out of the way, let's continue. Next, we take the number 23,422,345 and divide it by 2:

23,422,345 ÷ 2 = 11,711,172.5

If the quotient is a whole number, then 2 and 11,711,172.5 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 23,422,345
-1 -23,422,345

Now, we try dividing 23,422,345 by 3:

23,422,345 ÷ 3 = 7,807,448.3333

If the quotient is a whole number, then 3 and 7,807,448.3333 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 23,422,345
-1 -23,422,345

Let's try dividing by 4:

23,422,345 ÷ 4 = 5,855,586.25

If the quotient is a whole number, then 4 and 5,855,586.25 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 23,422,345
-1 23,422,345
Keep dividing by the next highest number until you cannot divide anymore.

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

15171985953231,61514,50372,515246,551275,5571,232,7551,377,7854,684,46923,422,345
-1-5-17-19-85-95-323-1,615-14,503-72,515-246,551-275,557-1,232,755-1,377,785-4,684,469-23,422,345

More Examples

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