Q: What are the factor combinations of the number 120,231,311?

 A:
Positive:   1 x 12023131141 x 293247143 x 279607747 x 25581131451 x 828611763 x 681971927 x 623932021 x 59491
Negative: -1 x -120231311-41 x -2932471-43 x -2796077-47 x -2558113-1451 x -82861-1763 x -68197-1927 x -62393-2021 x -59491


How do I find the factor combinations of the number 120,231,311?

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 120,231,311, 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.

1 120,231,311
-1 -120,231,311

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 120,231,311.

Example:
1 x 120,231,311 = 120,231,311
and
-1 x -120,231,311 = 120,231,311
Notice both answers equal 120,231,311

With that explanation out of the way, let's continue. Next, we take the number 120,231,311 and divide it by 2:

120,231,311 ÷ 2 = 60,115,655.5

If the quotient is a whole number, then 2 and 60,115,655.5 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:

1 120,231,311
-1 -120,231,311

Now, we try dividing 120,231,311 by 3:

120,231,311 ÷ 3 = 40,077,103.6667

If the quotient is a whole number, then 3 and 40,077,103.6667 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:

1 120,231,311
-1 -120,231,311

Let's try dividing by 4:

120,231,311 ÷ 4 = 30,057,827.75

If the quotient is a whole number, then 4 and 30,057,827.75 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:

1 120,231,311
-1 120,231,311
Keep dividing by the next highest number until you cannot divide anymore.

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

14143471,4511,7631,9272,02159,49162,39368,19782,8612,558,1132,796,0772,932,471120,231,311
-1-41-43-47-1,451-1,763-1,927-2,021-59,491-62,393-68,197-82,861-2,558,113-2,796,077-2,932,471-120,231,311

More Examples

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