Q: What are the factor combinations of the number 443,978?

 A:
Positive:   1 x 4439782 x 221989
Negative: -1 x -443978-2 x -221989


How do I find the factor combinations of the number 443,978?

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 443,978, 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.

1 443,978
-1 -443,978

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 443,978.

Example:
1 x 443,978 = 443,978
and
-1 x -443,978 = 443,978
Notice both answers equal 443,978

With that explanation out of the way, let's continue. Next, we take the number 443,978 and divide it by 2:

443,978 ÷ 2 = 221,989

If the quotient is a whole number, then 2 and 221,989 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 2 221,989 443,978
-1 -2 -221,989 -443,978

Now, we try dividing 443,978 by 3:

443,978 ÷ 3 = 147,992.6667

If the quotient is a whole number, then 3 and 147,992.6667 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 2 221,989 443,978
-1 -2 -221,989 -443,978

Let's try dividing by 4:

443,978 ÷ 4 = 110,994.5

If the quotient is a whole number, then 4 and 110,994.5 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 2 221,989 443,978
-1 -2 -221,989 443,978
Keep dividing by the next highest number until you cannot divide anymore.

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

12221,989443,978
-1-2-221,989-443,978

More Examples

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