Q: What are the factor combinations of the number 422,040,311?

 A:
Positive:   1 x 4220403117 x 6029147311 x 3836730177 x 54810431879 x 2246092917 x 14468313153 x 3208720419 x 20669
Negative: -1 x -422040311-7 x -60291473-11 x -38367301-77 x -5481043-1879 x -224609-2917 x -144683-13153 x -32087-20419 x -20669


How do I find the factor combinations of the number 422,040,311?

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 422,040,311, 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.

1 422,040,311
-1 -422,040,311

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 422,040,311.

Example:
1 x 422,040,311 = 422,040,311
and
-1 x -422,040,311 = 422,040,311
Notice both answers equal 422,040,311

With that explanation out of the way, let's continue. Next, we take the number 422,040,311 and divide it by 2:

422,040,311 ÷ 2 = 211,020,155.5

If the quotient is a whole number, then 2 and 211,020,155.5 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:

1 422,040,311
-1 -422,040,311

Now, we try dividing 422,040,311 by 3:

422,040,311 ÷ 3 = 140,680,103.6667

If the quotient is a whole number, then 3 and 140,680,103.6667 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:

1 422,040,311
-1 -422,040,311

Let's try dividing by 4:

422,040,311 ÷ 4 = 105,510,077.75

If the quotient is a whole number, then 4 and 105,510,077.75 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:

1 422,040,311
-1 422,040,311
Keep dividing by the next highest number until you cannot divide anymore.

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

1711771,8792,91713,15320,41920,66932,087144,683224,6095,481,04338,367,30160,291,473422,040,311
-1-7-11-77-1,879-2,917-13,153-20,419-20,669-32,087-144,683-224,609-5,481,043-38,367,301-60,291,473-422,040,311

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