Q: What are the factor combinations of the number 123,200,335?

 A:
Positive:   1 x 1232003355 x 24640067107 x 1151405535 x 230281
Negative: -1 x -123200335-5 x -24640067-107 x -1151405-535 x -230281


How do I find the factor combinations of the number 123,200,335?

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 123,200,335, 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.

1 123,200,335
-1 -123,200,335

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 123,200,335.

Example:
1 x 123,200,335 = 123,200,335
and
-1 x -123,200,335 = 123,200,335
Notice both answers equal 123,200,335

With that explanation out of the way, let's continue. Next, we take the number 123,200,335 and divide it by 2:

123,200,335 ÷ 2 = 61,600,167.5

If the quotient is a whole number, then 2 and 61,600,167.5 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:

1 123,200,335
-1 -123,200,335

Now, we try dividing 123,200,335 by 3:

123,200,335 ÷ 3 = 41,066,778.3333

If the quotient is a whole number, then 3 and 41,066,778.3333 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:

1 123,200,335
-1 -123,200,335

Let's try dividing by 4:

123,200,335 ÷ 4 = 30,800,083.75

If the quotient is a whole number, then 4 and 30,800,083.75 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:

1 123,200,335
-1 123,200,335
Keep dividing by the next highest number until you cannot divide anymore.

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

15107535230,2811,151,40524,640,067123,200,335
-1-5-107-535-230,281-1,151,405-24,640,067-123,200,335

More Examples

Here are some more numbers to try:

123,200,333123,200,334123,200,336123,200,337
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