Q: What are the factor combinations of the number 40,215,217?

 A:
Positive:   1 x 402152177 x 574503117 x 2365601103 x 390439119 x 337943193 x 208369289 x 139153721 x 557771351 x 297671751 x 229672023 x 198793281 x 12257
Negative: -1 x -40215217-7 x -5745031-17 x -2365601-103 x -390439-119 x -337943-193 x -208369-289 x -139153-721 x -55777-1351 x -29767-1751 x -22967-2023 x -19879-3281 x -12257


How do I find the factor combinations of the number 40,215,217?

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 40,215,217, 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 40,215,217
-1 -40,215,217

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 40,215,217.

Example:
1 x 40,215,217 = 40,215,217
and
-1 x -40,215,217 = 40,215,217
Notice both answers equal 40,215,217

With that explanation out of the way, let's continue. Next, we take the number 40,215,217 and divide it by 2:

40,215,217 ÷ 2 = 20,107,608.5

If the quotient is a whole number, then 2 and 20,107,608.5 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 40,215,217
-1 -40,215,217

Now, we try dividing 40,215,217 by 3:

40,215,217 ÷ 3 = 13,405,072.3333

If the quotient is a whole number, then 3 and 13,405,072.3333 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 40,215,217
-1 -40,215,217

Let's try dividing by 4:

40,215,217 ÷ 4 = 10,053,804.25

If the quotient is a whole number, then 4 and 10,053,804.25 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 40,215,217
-1 40,215,217
Keep dividing by the next highest number until you cannot divide anymore.

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

17171031191932897211,3511,7512,0233,28112,25719,87922,96729,76755,777139,153208,369337,943390,4392,365,6015,745,03140,215,217
-1-7-17-103-119-193-289-721-1,351-1,751-2,023-3,281-12,257-19,879-22,967-29,767-55,777-139,153-208,369-337,943-390,439-2,365,601-5,745,031-40,215,217

More Examples

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