Q: What are the factor combinations of the number 40,344,005?

 A:
Positive:   1 x 403440055 x 806880113 x 310338565 x 620677571 x 706551087 x 371152855 x 141315435 x 7423
Negative: -1 x -40344005-5 x -8068801-13 x -3103385-65 x -620677-571 x -70655-1087 x -37115-2855 x -14131-5435 x -7423


How do I find the factor combinations of the number 40,344,005?

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 40,344,005, 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 40,344,005
-1 -40,344,005

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 40,344,005.

Example:
1 x 40,344,005 = 40,344,005
and
-1 x -40,344,005 = 40,344,005
Notice both answers equal 40,344,005

With that explanation out of the way, let's continue. Next, we take the number 40,344,005 and divide it by 2:

40,344,005 ÷ 2 = 20,172,002.5

If the quotient is a whole number, then 2 and 20,172,002.5 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 40,344,005
-1 -40,344,005

Now, we try dividing 40,344,005 by 3:

40,344,005 ÷ 3 = 13,448,001.6667

If the quotient is a whole number, then 3 and 13,448,001.6667 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 40,344,005
-1 -40,344,005

Let's try dividing by 4:

40,344,005 ÷ 4 = 10,086,001.25

If the quotient is a whole number, then 4 and 10,086,001.25 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 40,344,005
-1 40,344,005
Keep dividing by the next highest number until you cannot divide anymore.

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

1513655711,0872,8555,4357,42314,13137,11570,655620,6773,103,3858,068,80140,344,005
-1-5-13-65-571-1,087-2,855-5,435-7,423-14,131-37,115-70,655-620,677-3,103,385-8,068,801-40,344,005

More Examples

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