Q: What are the factor combinations of the number 131,221,343?

 A:
Positive:   1 x 13122134311 x 119292132543 x 516014691 x 27973
Negative: -1 x -131221343-11 x -11929213-2543 x -51601-4691 x -27973


How do I find the factor combinations of the number 131,221,343?

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 131,221,343, 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.

1 131,221,343
-1 -131,221,343

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 131,221,343.

Example:
1 x 131,221,343 = 131,221,343
and
-1 x -131,221,343 = 131,221,343
Notice both answers equal 131,221,343

With that explanation out of the way, let's continue. Next, we take the number 131,221,343 and divide it by 2:

131,221,343 ÷ 2 = 65,610,671.5

If the quotient is a whole number, then 2 and 65,610,671.5 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:

1 131,221,343
-1 -131,221,343

Now, we try dividing 131,221,343 by 3:

131,221,343 ÷ 3 = 43,740,447.6667

If the quotient is a whole number, then 3 and 43,740,447.6667 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:

1 131,221,343
-1 -131,221,343

Let's try dividing by 4:

131,221,343 ÷ 4 = 32,805,335.75

If the quotient is a whole number, then 4 and 32,805,335.75 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:

1 131,221,343
-1 131,221,343
Keep dividing by the next highest number until you cannot divide anymore.

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

1112,5434,69127,97351,60111,929,213131,221,343
-1-11-2,543-4,691-27,973-51,601-11,929,213-131,221,343

More Examples

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