Q: What are the factor combinations of the number 31,204,571?

 A:
Positive:   1 x 3120457117 x 183556371 x 439501103 x 302957251 x 1243211207 x 258531751 x 178214267 x 7313
Negative: -1 x -31204571-17 x -1835563-71 x -439501-103 x -302957-251 x -124321-1207 x -25853-1751 x -17821-4267 x -7313


How do I find the factor combinations of the number 31,204,571?

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 31,204,571, 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 31,204,571
-1 -31,204,571

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 31,204,571.

Example:
1 x 31,204,571 = 31,204,571
and
-1 x -31,204,571 = 31,204,571
Notice both answers equal 31,204,571

With that explanation out of the way, let's continue. Next, we take the number 31,204,571 and divide it by 2:

31,204,571 ÷ 2 = 15,602,285.5

If the quotient is a whole number, then 2 and 15,602,285.5 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 31,204,571
-1 -31,204,571

Now, we try dividing 31,204,571 by 3:

31,204,571 ÷ 3 = 10,401,523.6667

If the quotient is a whole number, then 3 and 10,401,523.6667 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 31,204,571
-1 -31,204,571

Let's try dividing by 4:

31,204,571 ÷ 4 = 7,801,142.75

If the quotient is a whole number, then 4 and 7,801,142.75 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 31,204,571
-1 31,204,571
Keep dividing by the next highest number until you cannot divide anymore.

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

117711032511,2071,7514,2677,31317,82125,853124,321302,957439,5011,835,56331,204,571
-1-17-71-103-251-1,207-1,751-4,267-7,313-17,821-25,853-124,321-302,957-439,501-1,835,563-31,204,571

More Examples

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