Q: What are the factor combinations of the number 821,315?

 A:
Positive:   1 x 8213155 x 16426311 x 7466555 x 14933109 x 7535137 x 5995545 x 1507685 x 1199
Negative: -1 x -821315-5 x -164263-11 x -74665-55 x -14933-109 x -7535-137 x -5995-545 x -1507-685 x -1199


How do I find the factor combinations of the number 821,315?

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 821,315, 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.

1 821,315
-1 -821,315

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 821,315.

Example:
1 x 821,315 = 821,315
and
-1 x -821,315 = 821,315
Notice both answers equal 821,315

With that explanation out of the way, let's continue. Next, we take the number 821,315 and divide it by 2:

821,315 ÷ 2 = 410,657.5

If the quotient is a whole number, then 2 and 410,657.5 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:

1 821,315
-1 -821,315

Now, we try dividing 821,315 by 3:

821,315 ÷ 3 = 273,771.6667

If the quotient is a whole number, then 3 and 273,771.6667 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:

1 821,315
-1 -821,315

Let's try dividing by 4:

821,315 ÷ 4 = 205,328.75

If the quotient is a whole number, then 4 and 205,328.75 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:

1 821,315
-1 821,315
Keep dividing by the next highest number until you cannot divide anymore.

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

1511551091375456851,1991,5075,9957,53514,93374,665164,263821,315
-1-5-11-55-109-137-545-685-1,199-1,507-5,995-7,535-14,933-74,665-164,263-821,315

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