Q: What are the factor combinations of the number 40,314,131?

 A:
Positive:   1 x 4031413111 x 366492113 x 3101087143 x 281917151 x 2669811661 x 242711867 x 215931963 x 20537
Negative: -1 x -40314131-11 x -3664921-13 x -3101087-143 x -281917-151 x -266981-1661 x -24271-1867 x -21593-1963 x -20537


How do I find the factor combinations of the number 40,314,131?

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 40,314,131, 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 40,314,131
-1 -40,314,131

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 40,314,131.

Example:
1 x 40,314,131 = 40,314,131
and
-1 x -40,314,131 = 40,314,131
Notice both answers equal 40,314,131

With that explanation out of the way, let's continue. Next, we take the number 40,314,131 and divide it by 2:

40,314,131 ÷ 2 = 20,157,065.5

If the quotient is a whole number, then 2 and 20,157,065.5 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 40,314,131
-1 -40,314,131

Now, we try dividing 40,314,131 by 3:

40,314,131 ÷ 3 = 13,438,043.6667

If the quotient is a whole number, then 3 and 13,438,043.6667 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 40,314,131
-1 -40,314,131

Let's try dividing by 4:

40,314,131 ÷ 4 = 10,078,532.75

If the quotient is a whole number, then 4 and 10,078,532.75 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 40,314,131
-1 40,314,131
Keep dividing by the next highest number until you cannot divide anymore.

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

111131431511,6611,8671,96320,53721,59324,271266,981281,9173,101,0873,664,92140,314,131
-1-11-13-143-151-1,661-1,867-1,963-20,537-21,593-24,271-266,981-281,917-3,101,087-3,664,921-40,314,131

More Examples

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