Q: What are the factor combinations of the number 214,513,531?

 A:
Positive:   1 x 21451353117 x 1261844337 x 5797663257 x 834683629 x 3410391327 x 1616534369 x 490999509 x 22559
Negative: -1 x -214513531-17 x -12618443-37 x -5797663-257 x -834683-629 x -341039-1327 x -161653-4369 x -49099-9509 x -22559


How do I find the factor combinations of the number 214,513,531?

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 214,513,531, 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.

1 214,513,531
-1 -214,513,531

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 214,513,531.

Example:
1 x 214,513,531 = 214,513,531
and
-1 x -214,513,531 = 214,513,531
Notice both answers equal 214,513,531

With that explanation out of the way, let's continue. Next, we take the number 214,513,531 and divide it by 2:

214,513,531 ÷ 2 = 107,256,765.5

If the quotient is a whole number, then 2 and 107,256,765.5 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:

1 214,513,531
-1 -214,513,531

Now, we try dividing 214,513,531 by 3:

214,513,531 ÷ 3 = 71,504,510.3333

If the quotient is a whole number, then 3 and 71,504,510.3333 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:

1 214,513,531
-1 -214,513,531

Let's try dividing by 4:

214,513,531 ÷ 4 = 53,628,382.75

If the quotient is a whole number, then 4 and 53,628,382.75 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:

1 214,513,531
-1 214,513,531
Keep dividing by the next highest number until you cannot divide anymore.

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

117372576291,3274,3699,50922,55949,099161,653341,039834,6835,797,66312,618,443214,513,531
-1-17-37-257-629-1,327-4,369-9,509-22,559-49,099-161,653-341,039-834,683-5,797,663-12,618,443-214,513,531

More Examples

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