Q: What are the factor combinations of the number 40,134,017?

 A:
Positive:   1 x 401340177 x 573343111 x 364854777 x 521221233 x 1722491631 x 246072237 x 179412563 x 15659
Negative: -1 x -40134017-7 x -5733431-11 x -3648547-77 x -521221-233 x -172249-1631 x -24607-2237 x -17941-2563 x -15659


How do I find the factor combinations of the number 40,134,017?

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 40,134,017, 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 40,134,017
-1 -40,134,017

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 40,134,017.

Example:
1 x 40,134,017 = 40,134,017
and
-1 x -40,134,017 = 40,134,017
Notice both answers equal 40,134,017

With that explanation out of the way, let's continue. Next, we take the number 40,134,017 and divide it by 2:

40,134,017 ÷ 2 = 20,067,008.5

If the quotient is a whole number, then 2 and 20,067,008.5 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 40,134,017
-1 -40,134,017

Now, we try dividing 40,134,017 by 3:

40,134,017 ÷ 3 = 13,378,005.6667

If the quotient is a whole number, then 3 and 13,378,005.6667 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 40,134,017
-1 -40,134,017

Let's try dividing by 4:

40,134,017 ÷ 4 = 10,033,504.25

If the quotient is a whole number, then 4 and 10,033,504.25 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 40,134,017
-1 40,134,017
Keep dividing by the next highest number until you cannot divide anymore.

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

1711772331,6312,2372,56315,65917,94124,607172,249521,2213,648,5475,733,43140,134,017
-1-7-11-77-233-1,631-2,237-2,563-15,659-17,941-24,607-172,249-521,221-3,648,547-5,733,431-40,134,017

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