Q: What are the factor combinations of the number 821,729?
A:
Positive:
1 x 82172917 x 48337
Negative:
-1 x -821729-17 x -48337
A:
Positive:
1 x 82172917 x 48337
Negative:
-1 x -821729-17 x -48337
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 821,729, it is easier to work with a table - it's called factoring from the outside in.
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 | 821,729 | |
-1 | -821,729 |
When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 821,729.
Example:
1 x 821,729 = 821,729
and
-1 x -821,729 = 821,729
Notice both answers equal 821,729
With that explanation out of the way, let's continue. Next, we take the number 821,729 and divide it by 2:
821,729 ÷ 2 = 410,864.5
If the quotient is a whole number, then 2 and 410,864.5 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 | 821,729 | |
-1 | -821,729 |
Now, we try dividing 821,729 by 3:
821,729 ÷ 3 = 273,909.6667
If the quotient is a whole number, then 3 and 273,909.6667 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 | 821,729 | |
-1 | -821,729 |
Let's try dividing by 4:
821,729 ÷ 4 = 205,432.25
If the quotient is a whole number, then 4 and 205,432.25 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 | 821,729 | |
-1 | 821,729 |
If you did it right, you will end up with this table:
1 | 17 | 48,337 | 821,729 |
-1 | -17 | -48,337 | -821,729 |
Here are some more numbers to try:
Try the factor calculator