Q: What are the factor combinations of the number 422,022,331?

 A:
Positive:   1 x 42202233117 x 2482484323 x 18348797191 x 2209541391 x 10793413247 x 1299734393 x 960675651 x 74681
Negative: -1 x -422022331-17 x -24824843-23 x -18348797-191 x -2209541-391 x -1079341-3247 x -129973-4393 x -96067-5651 x -74681


How do I find the factor combinations of the number 422,022,331?

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 422,022,331, 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.

1 422,022,331
-1 -422,022,331

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 422,022,331.

Example:
1 x 422,022,331 = 422,022,331
and
-1 x -422,022,331 = 422,022,331
Notice both answers equal 422,022,331

With that explanation out of the way, let's continue. Next, we take the number 422,022,331 and divide it by 2:

422,022,331 ÷ 2 = 211,011,165.5

If the quotient is a whole number, then 2 and 211,011,165.5 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:

1 422,022,331
-1 -422,022,331

Now, we try dividing 422,022,331 by 3:

422,022,331 ÷ 3 = 140,674,110.3333

If the quotient is a whole number, then 3 and 140,674,110.3333 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:

1 422,022,331
-1 -422,022,331

Let's try dividing by 4:

422,022,331 ÷ 4 = 105,505,582.75

If the quotient is a whole number, then 4 and 105,505,582.75 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:

1 422,022,331
-1 422,022,331
Keep dividing by the next highest number until you cannot divide anymore.

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

117231913913,2474,3935,65174,68196,067129,9731,079,3412,209,54118,348,79724,824,843422,022,331
-1-17-23-191-391-3,247-4,393-5,651-74,681-96,067-129,973-1,079,341-2,209,541-18,348,797-24,824,843-422,022,331

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