Q: What are the factor combinations of the number 3,627,239?

 A:
Positive:   1 x 36272397 x 51817711 x 32974917 x 21336777 x 47107119 x 30481163 x 22253187 x 19397289 x 125511141 x 31791309 x 27711793 x 2023
Negative: -1 x -3627239-7 x -518177-11 x -329749-17 x -213367-77 x -47107-119 x -30481-163 x -22253-187 x -19397-289 x -12551-1141 x -3179-1309 x -2771-1793 x -2023


How do I find the factor combinations of the number 3,627,239?

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 3,627,239, 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 3,627,239
-1 -3,627,239

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 3,627,239.

Example:
1 x 3,627,239 = 3,627,239
and
-1 x -3,627,239 = 3,627,239
Notice both answers equal 3,627,239

With that explanation out of the way, let's continue. Next, we take the number 3,627,239 and divide it by 2:

3,627,239 ÷ 2 = 1,813,619.5

If the quotient is a whole number, then 2 and 1,813,619.5 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 3,627,239
-1 -3,627,239

Now, we try dividing 3,627,239 by 3:

3,627,239 ÷ 3 = 1,209,079.6667

If the quotient is a whole number, then 3 and 1,209,079.6667 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 3,627,239
-1 -3,627,239

Let's try dividing by 4:

3,627,239 ÷ 4 = 906,809.75

If the quotient is a whole number, then 4 and 906,809.75 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 3,627,239
-1 3,627,239
Keep dividing by the next highest number until you cannot divide anymore.

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

171117771191631872891,1411,3091,7932,0232,7713,17912,55119,39722,25330,48147,107213,367329,749518,1773,627,239
-1-7-11-17-77-119-163-187-289-1,141-1,309-1,793-2,023-2,771-3,179-12,551-19,397-22,253-30,481-47,107-213,367-329,749-518,177-3,627,239

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