Q: What are the factor combinations of the number 32,716,229?

 A:
Positive:   1 x 327162297 x 467374713 x 251663391 x 359519233 x 1404131543 x 212031631 x 200593029 x 10801
Negative: -1 x -32716229-7 x -4673747-13 x -2516633-91 x -359519-233 x -140413-1543 x -21203-1631 x -20059-3029 x -10801


How do I find the factor combinations of the number 32,716,229?

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 32,716,229, 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 32,716,229
-1 -32,716,229

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 32,716,229.

Example:
1 x 32,716,229 = 32,716,229
and
-1 x -32,716,229 = 32,716,229
Notice both answers equal 32,716,229

With that explanation out of the way, let's continue. Next, we take the number 32,716,229 and divide it by 2:

32,716,229 ÷ 2 = 16,358,114.5

If the quotient is a whole number, then 2 and 16,358,114.5 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 32,716,229
-1 -32,716,229

Now, we try dividing 32,716,229 by 3:

32,716,229 ÷ 3 = 10,905,409.6667

If the quotient is a whole number, then 3 and 10,905,409.6667 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 32,716,229
-1 -32,716,229

Let's try dividing by 4:

32,716,229 ÷ 4 = 8,179,057.25

If the quotient is a whole number, then 4 and 8,179,057.25 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 32,716,229
-1 32,716,229
Keep dividing by the next highest number until you cannot divide anymore.

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

1713912331,5431,6313,02910,80120,05921,203140,413359,5192,516,6334,673,74732,716,229
-1-7-13-91-233-1,543-1,631-3,029-10,801-20,059-21,203-140,413-359,519-2,516,633-4,673,747-32,716,229

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