Q: What are the factor combinations of the number 34,322,921?

 A:
Positive:   1 x 3432292129 x 118354931 x 110719173 x 470177523 x 65627899 x 381792117 x 162132263 x 15167
Negative: -1 x -34322921-29 x -1183549-31 x -1107191-73 x -470177-523 x -65627-899 x -38179-2117 x -16213-2263 x -15167


How do I find the factor combinations of the number 34,322,921?

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 34,322,921, 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 34,322,921
-1 -34,322,921

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 34,322,921.

Example:
1 x 34,322,921 = 34,322,921
and
-1 x -34,322,921 = 34,322,921
Notice both answers equal 34,322,921

With that explanation out of the way, let's continue. Next, we take the number 34,322,921 and divide it by 2:

34,322,921 ÷ 2 = 17,161,460.5

If the quotient is a whole number, then 2 and 17,161,460.5 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 34,322,921
-1 -34,322,921

Now, we try dividing 34,322,921 by 3:

34,322,921 ÷ 3 = 11,440,973.6667

If the quotient is a whole number, then 3 and 11,440,973.6667 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 34,322,921
-1 -34,322,921

Let's try dividing by 4:

34,322,921 ÷ 4 = 8,580,730.25

If the quotient is a whole number, then 4 and 8,580,730.25 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 34,322,921
-1 34,322,921
Keep dividing by the next highest number until you cannot divide anymore.

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

12931735238992,1172,26315,16716,21338,17965,627470,1771,107,1911,183,54934,322,921
-1-29-31-73-523-899-2,117-2,263-15,167-16,213-38,179-65,627-470,177-1,107,191-1,183,549-34,322,921

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