Q: What are the factor combinations of the number 105,501,131?

 A:
Positive:   1 x 1055011318599 x 12269
Negative: -1 x -105501131-8599 x -12269


How do I find the factor combinations of the number 105,501,131?

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 105,501,131, 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.

1 105,501,131
-1 -105,501,131

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 105,501,131.

Example:
1 x 105,501,131 = 105,501,131
and
-1 x -105,501,131 = 105,501,131
Notice both answers equal 105,501,131

With that explanation out of the way, let's continue. Next, we take the number 105,501,131 and divide it by 2:

105,501,131 ÷ 2 = 52,750,565.5

If the quotient is a whole number, then 2 and 52,750,565.5 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:

1 105,501,131
-1 -105,501,131

Now, we try dividing 105,501,131 by 3:

105,501,131 ÷ 3 = 35,167,043.6667

If the quotient is a whole number, then 3 and 35,167,043.6667 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:

1 105,501,131
-1 -105,501,131

Let's try dividing by 4:

105,501,131 ÷ 4 = 26,375,282.75

If the quotient is a whole number, then 4 and 26,375,282.75 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:

1 105,501,131
-1 105,501,131
Keep dividing by the next highest number until you cannot divide anymore.

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

18,59912,269105,501,131
-1-8,599-12,269-105,501,131

More Examples

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