Q: What are the factor combinations of the number 131,310,311?

 A:
Positive:   1 x 13131031111 x 1193730119 x 691106971 x 1849441209 x 628279781 x 1681311349 x 973398849 x 14839
Negative: -1 x -131310311-11 x -11937301-19 x -6911069-71 x -1849441-209 x -628279-781 x -168131-1349 x -97339-8849 x -14839


How do I find the factor combinations of the number 131,310,311?

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 131,310,311, 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.

1 131,310,311
-1 -131,310,311

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 131,310,311.

Example:
1 x 131,310,311 = 131,310,311
and
-1 x -131,310,311 = 131,310,311
Notice both answers equal 131,310,311

With that explanation out of the way, let's continue. Next, we take the number 131,310,311 and divide it by 2:

131,310,311 ÷ 2 = 65,655,155.5

If the quotient is a whole number, then 2 and 65,655,155.5 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:

1 131,310,311
-1 -131,310,311

Now, we try dividing 131,310,311 by 3:

131,310,311 ÷ 3 = 43,770,103.6667

If the quotient is a whole number, then 3 and 43,770,103.6667 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:

1 131,310,311
-1 -131,310,311

Let's try dividing by 4:

131,310,311 ÷ 4 = 32,827,577.75

If the quotient is a whole number, then 4 and 32,827,577.75 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:

1 131,310,311
-1 131,310,311
Keep dividing by the next highest number until you cannot divide anymore.

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

11119712097811,3498,84914,83997,339168,131628,2791,849,4416,911,06911,937,301131,310,311
-1-11-19-71-209-781-1,349-8,849-14,839-97,339-168,131-628,279-1,849,441-6,911,069-11,937,301-131,310,311

More Examples

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