Q: What are the factor combinations of the number 131,540,315?

 A:
Positive:   1 x 1315403155 x 26308063251 x 524065281 x 468115373 x 3526551255 x 1048131405 x 936231865 x 70531
Negative: -1 x -131540315-5 x -26308063-251 x -524065-281 x -468115-373 x -352655-1255 x -104813-1405 x -93623-1865 x -70531


How do I find the factor combinations of the number 131,540,315?

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 131,540,315, 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.

1 131,540,315
-1 -131,540,315

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 131,540,315.

Example:
1 x 131,540,315 = 131,540,315
and
-1 x -131,540,315 = 131,540,315
Notice both answers equal 131,540,315

With that explanation out of the way, let's continue. Next, we take the number 131,540,315 and divide it by 2:

131,540,315 ÷ 2 = 65,770,157.5

If the quotient is a whole number, then 2 and 65,770,157.5 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:

1 131,540,315
-1 -131,540,315

Now, we try dividing 131,540,315 by 3:

131,540,315 ÷ 3 = 43,846,771.6667

If the quotient is a whole number, then 3 and 43,846,771.6667 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:

1 131,540,315
-1 -131,540,315

Let's try dividing by 4:

131,540,315 ÷ 4 = 32,885,078.75

If the quotient is a whole number, then 4 and 32,885,078.75 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:

1 131,540,315
-1 131,540,315
Keep dividing by the next highest number until you cannot divide anymore.

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

152512813731,2551,4051,86570,53193,623104,813352,655468,115524,06526,308,063131,540,315
-1-5-251-281-373-1,255-1,405-1,865-70,531-93,623-104,813-352,655-468,115-524,065-26,308,063-131,540,315

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