Q: What are the factor combinations of the number 31,211,125?

 A:
Positive:   1 x 312111255 x 624222511 x 283737525 x 124844555 x 567475125 x 249689275 x 1134951375 x 22699
Negative: -1 x -31211125-5 x -6242225-11 x -2837375-25 x -1248445-55 x -567475-125 x -249689-275 x -113495-1375 x -22699


How do I find the factor combinations of the number 31,211,125?

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 31,211,125, 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 31,211,125
-1 -31,211,125

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 31,211,125.

Example:
1 x 31,211,125 = 31,211,125
and
-1 x -31,211,125 = 31,211,125
Notice both answers equal 31,211,125

With that explanation out of the way, let's continue. Next, we take the number 31,211,125 and divide it by 2:

31,211,125 ÷ 2 = 15,605,562.5

If the quotient is a whole number, then 2 and 15,605,562.5 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 31,211,125
-1 -31,211,125

Now, we try dividing 31,211,125 by 3:

31,211,125 ÷ 3 = 10,403,708.3333

If the quotient is a whole number, then 3 and 10,403,708.3333 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 31,211,125
-1 -31,211,125

Let's try dividing by 4:

31,211,125 ÷ 4 = 7,802,781.25

If the quotient is a whole number, then 4 and 7,802,781.25 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 31,211,125
-1 31,211,125
Keep dividing by the next highest number until you cannot divide anymore.

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

151125551252751,37522,699113,495249,689567,4751,248,4452,837,3756,242,22531,211,125
-1-5-11-25-55-125-275-1,375-22,699-113,495-249,689-567,475-1,248,445-2,837,375-6,242,225-31,211,125

More Examples

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