Q: What are the factor combinations of the number 7,312,873?

 A:
Positive:   1 x 731287317 x 43016923 x 31795159 x 123947317 x 23069391 x 187031003 x 72911357 x 5389
Negative: -1 x -7312873-17 x -430169-23 x -317951-59 x -123947-317 x -23069-391 x -18703-1003 x -7291-1357 x -5389


How do I find the factor combinations of the number 7,312,873?

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 7,312,873, 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 7,312,873
-1 -7,312,873

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 7,312,873.

Example:
1 x 7,312,873 = 7,312,873
and
-1 x -7,312,873 = 7,312,873
Notice both answers equal 7,312,873

With that explanation out of the way, let's continue. Next, we take the number 7,312,873 and divide it by 2:

7,312,873 ÷ 2 = 3,656,436.5

If the quotient is a whole number, then 2 and 3,656,436.5 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 7,312,873
-1 -7,312,873

Now, we try dividing 7,312,873 by 3:

7,312,873 ÷ 3 = 2,437,624.3333

If the quotient is a whole number, then 3 and 2,437,624.3333 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 7,312,873
-1 -7,312,873

Let's try dividing by 4:

7,312,873 ÷ 4 = 1,828,218.25

If the quotient is a whole number, then 4 and 1,828,218.25 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 7,312,873
-1 7,312,873
Keep dividing by the next highest number until you cannot divide anymore.

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

11723593173911,0031,3575,3897,29118,70323,069123,947317,951430,1697,312,873
-1-17-23-59-317-391-1,003-1,357-5,389-7,291-18,703-23,069-123,947-317,951-430,169-7,312,873

More Examples

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