Q: What are the factor combinations of the number 31,499,249?

 A:
Positive:   1 x 3149924917 x 185289729 x 1086181181 x 174029353 x 89233493 x 638933077 x 102375249 x 6001
Negative: -1 x -31499249-17 x -1852897-29 x -1086181-181 x -174029-353 x -89233-493 x -63893-3077 x -10237-5249 x -6001


How do I find the factor combinations of the number 31,499,249?

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 31,499,249, 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 31,499,249
-1 -31,499,249

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 31,499,249.

Example:
1 x 31,499,249 = 31,499,249
and
-1 x -31,499,249 = 31,499,249
Notice both answers equal 31,499,249

With that explanation out of the way, let's continue. Next, we take the number 31,499,249 and divide it by 2:

31,499,249 ÷ 2 = 15,749,624.5

If the quotient is a whole number, then 2 and 15,749,624.5 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 31,499,249
-1 -31,499,249

Now, we try dividing 31,499,249 by 3:

31,499,249 ÷ 3 = 10,499,749.6667

If the quotient is a whole number, then 3 and 10,499,749.6667 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 31,499,249
-1 -31,499,249

Let's try dividing by 4:

31,499,249 ÷ 4 = 7,874,812.25

If the quotient is a whole number, then 4 and 7,874,812.25 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 31,499,249
-1 31,499,249
Keep dividing by the next highest number until you cannot divide anymore.

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

117291813534933,0775,2496,00110,23763,89389,233174,0291,086,1811,852,89731,499,249
-1-17-29-181-353-493-3,077-5,249-6,001-10,237-63,893-89,233-174,029-1,086,181-1,852,897-31,499,249

More Examples

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