Q: What are the factor combinations of the number 34,231,421?

 A:
Positive:   1 x 342314217 x 489020317 x 2013613119 x 287659307 x 111503937 x 365332149 x 159295219 x 6559
Negative: -1 x -34231421-7 x -4890203-17 x -2013613-119 x -287659-307 x -111503-937 x -36533-2149 x -15929-5219 x -6559


How do I find the factor combinations of the number 34,231,421?

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 34,231,421, 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 34,231,421
-1 -34,231,421

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 34,231,421.

Example:
1 x 34,231,421 = 34,231,421
and
-1 x -34,231,421 = 34,231,421
Notice both answers equal 34,231,421

With that explanation out of the way, let's continue. Next, we take the number 34,231,421 and divide it by 2:

34,231,421 ÷ 2 = 17,115,710.5

If the quotient is a whole number, then 2 and 17,115,710.5 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 34,231,421
-1 -34,231,421

Now, we try dividing 34,231,421 by 3:

34,231,421 ÷ 3 = 11,410,473.6667

If the quotient is a whole number, then 3 and 11,410,473.6667 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 34,231,421
-1 -34,231,421

Let's try dividing by 4:

34,231,421 ÷ 4 = 8,557,855.25

If the quotient is a whole number, then 4 and 8,557,855.25 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 34,231,421
-1 34,231,421
Keep dividing by the next highest number until you cannot divide anymore.

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

17171193079372,1495,2196,55915,92936,533111,503287,6592,013,6134,890,20334,231,421
-1-7-17-119-307-937-2,149-5,219-6,559-15,929-36,533-111,503-287,659-2,013,613-4,890,203-34,231,421

More Examples

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