Q: What are the factor combinations of the number 3,401,531?

 A:
Positive:   1 x 34015317 x 48593347 x 7237349 x 69419211 x 16121329 x 10339343 x 99171477 x 2303
Negative: -1 x -3401531-7 x -485933-47 x -72373-49 x -69419-211 x -16121-329 x -10339-343 x -9917-1477 x -2303


How do I find the factor combinations of the number 3,401,531?

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 3,401,531, 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 3,401,531
-1 -3,401,531

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 3,401,531.

Example:
1 x 3,401,531 = 3,401,531
and
-1 x -3,401,531 = 3,401,531
Notice both answers equal 3,401,531

With that explanation out of the way, let's continue. Next, we take the number 3,401,531 and divide it by 2:

3,401,531 ÷ 2 = 1,700,765.5

If the quotient is a whole number, then 2 and 1,700,765.5 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 3,401,531
-1 -3,401,531

Now, we try dividing 3,401,531 by 3:

3,401,531 ÷ 3 = 1,133,843.6667

If the quotient is a whole number, then 3 and 1,133,843.6667 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 3,401,531
-1 -3,401,531

Let's try dividing by 4:

3,401,531 ÷ 4 = 850,382.75

If the quotient is a whole number, then 4 and 850,382.75 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 3,401,531
-1 3,401,531
Keep dividing by the next highest number until you cannot divide anymore.

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

1747492113293431,4772,3039,91710,33916,12169,41972,373485,9333,401,531
-1-7-47-49-211-329-343-1,477-2,303-9,917-10,339-16,121-69,419-72,373-485,933-3,401,531

More Examples

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