Q: What are the factor combinations of the number 827,976?

 A:
Positive:   1 x 8279762 x 4139883 x 2759924 x 2069946 x 1379968 x 10349712 x 6899824 x 34499
Negative: -1 x -827976-2 x -413988-3 x -275992-4 x -206994-6 x -137996-8 x -103497-12 x -68998-24 x -34499


How do I find the factor combinations of the number 827,976?

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 827,976, 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.

1 827,976
-1 -827,976

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 827,976.

Example:
1 x 827,976 = 827,976
and
-1 x -827,976 = 827,976
Notice both answers equal 827,976

With that explanation out of the way, let's continue. Next, we take the number 827,976 and divide it by 2:

827,976 ÷ 2 = 413,988

If the quotient is a whole number, then 2 and 413,988 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 413,988 827,976
-1 -2 -413,988 -827,976

Now, we try dividing 827,976 by 3:

827,976 ÷ 3 = 275,992

If the quotient is a whole number, then 3 and 275,992 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 275,992 413,988 827,976
-1 -2 -3 -275,992 -413,988 -827,976

Let's try dividing by 4:

827,976 ÷ 4 = 206,994

If the quotient is a whole number, then 4 and 206,994 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 4 206,994 275,992 413,988 827,976
-1 -2 -3 -4 -206,994 -275,992 -413,988 827,976
Keep dividing by the next highest number until you cannot divide anymore.

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

123468122434,49968,998103,497137,996206,994275,992413,988827,976
-1-2-3-4-6-8-12-24-34,499-68,998-103,497-137,996-206,994-275,992-413,988-827,976

More Examples

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