Q: What are the factor combinations of the number 40,406,605?

 A:
Positive:   1 x 404066055 x 808132147 x 859715139 x 290695235 x 171943695 x 581391237 x 326656185 x 6533
Negative: -1 x -40406605-5 x -8081321-47 x -859715-139 x -290695-235 x -171943-695 x -58139-1237 x -32665-6185 x -6533


How do I find the factor combinations of the number 40,406,605?

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 40,406,605, 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 40,406,605
-1 -40,406,605

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 40,406,605.

Example:
1 x 40,406,605 = 40,406,605
and
-1 x -40,406,605 = 40,406,605
Notice both answers equal 40,406,605

With that explanation out of the way, let's continue. Next, we take the number 40,406,605 and divide it by 2:

40,406,605 ÷ 2 = 20,203,302.5

If the quotient is a whole number, then 2 and 20,203,302.5 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 40,406,605
-1 -40,406,605

Now, we try dividing 40,406,605 by 3:

40,406,605 ÷ 3 = 13,468,868.3333

If the quotient is a whole number, then 3 and 13,468,868.3333 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 40,406,605
-1 -40,406,605

Let's try dividing by 4:

40,406,605 ÷ 4 = 10,101,651.25

If the quotient is a whole number, then 4 and 10,101,651.25 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 40,406,605
-1 40,406,605
Keep dividing by the next highest number until you cannot divide anymore.

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

15471392356951,2376,1856,53332,66558,139171,943290,695859,7158,081,32140,406,605
-1-5-47-139-235-695-1,237-6,185-6,533-32,665-58,139-171,943-290,695-859,715-8,081,321-40,406,605

More Examples

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