Q: What are the factor combinations of the number 34,231,337?

 A:
Positive:   1 x 342313377 x 489019123 x 1488319161 x 212617173 x 1978691211 x 282671229 x 278533979 x 8603
Negative: -1 x -34231337-7 x -4890191-23 x -1488319-161 x -212617-173 x -197869-1211 x -28267-1229 x -27853-3979 x -8603


How do I find the factor combinations of the number 34,231,337?

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 34,231,337, 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 34,231,337
-1 -34,231,337

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 34,231,337.

Example:
1 x 34,231,337 = 34,231,337
and
-1 x -34,231,337 = 34,231,337
Notice both answers equal 34,231,337

With that explanation out of the way, let's continue. Next, we take the number 34,231,337 and divide it by 2:

34,231,337 ÷ 2 = 17,115,668.5

If the quotient is a whole number, then 2 and 17,115,668.5 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 34,231,337
-1 -34,231,337

Now, we try dividing 34,231,337 by 3:

34,231,337 ÷ 3 = 11,410,445.6667

If the quotient is a whole number, then 3 and 11,410,445.6667 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 34,231,337
-1 -34,231,337

Let's try dividing by 4:

34,231,337 ÷ 4 = 8,557,834.25

If the quotient is a whole number, then 4 and 8,557,834.25 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 34,231,337
-1 34,231,337
Keep dividing by the next highest number until you cannot divide anymore.

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

17231611731,2111,2293,9798,60327,85328,267197,869212,6171,488,3194,890,19134,231,337
-1-7-23-161-173-1,211-1,229-3,979-8,603-27,853-28,267-197,869-212,617-1,488,319-4,890,191-34,231,337

More Examples

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