Q: What are the factor combinations of the number 40,500,109?

 A:
Positive:   1 x 4050010913 x 311539343 x 94186353 x 764153559 x 72451689 x 587811367 x 296272279 x 17771
Negative: -1 x -40500109-13 x -3115393-43 x -941863-53 x -764153-559 x -72451-689 x -58781-1367 x -29627-2279 x -17771


How do I find the factor combinations of the number 40,500,109?

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 40,500,109, 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 40,500,109
-1 -40,500,109

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 40,500,109.

Example:
1 x 40,500,109 = 40,500,109
and
-1 x -40,500,109 = 40,500,109
Notice both answers equal 40,500,109

With that explanation out of the way, let's continue. Next, we take the number 40,500,109 and divide it by 2:

40,500,109 ÷ 2 = 20,250,054.5

If the quotient is a whole number, then 2 and 20,250,054.5 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 40,500,109
-1 -40,500,109

Now, we try dividing 40,500,109 by 3:

40,500,109 ÷ 3 = 13,500,036.3333

If the quotient is a whole number, then 3 and 13,500,036.3333 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 40,500,109
-1 -40,500,109

Let's try dividing by 4:

40,500,109 ÷ 4 = 10,125,027.25

If the quotient is a whole number, then 4 and 10,125,027.25 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 40,500,109
-1 40,500,109
Keep dividing by the next highest number until you cannot divide anymore.

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

11343535596891,3672,27917,77129,62758,78172,451764,153941,8633,115,39340,500,109
-1-13-43-53-559-689-1,367-2,279-17,771-29,627-58,781-72,451-764,153-941,863-3,115,393-40,500,109

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