Q: What are the factor combinations of the number 784,817?

 A:
Positive:   1 x 78481711 x 71347
Negative: -1 x -784817-11 x -71347


How do I find the factor combinations of the number 784,817?

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 784,817, 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.

1 784,817
-1 -784,817

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 784,817.

Example:
1 x 784,817 = 784,817
and
-1 x -784,817 = 784,817
Notice both answers equal 784,817

With that explanation out of the way, let's continue. Next, we take the number 784,817 and divide it by 2:

784,817 ÷ 2 = 392,408.5

If the quotient is a whole number, then 2 and 392,408.5 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:

1 784,817
-1 -784,817

Now, we try dividing 784,817 by 3:

784,817 ÷ 3 = 261,605.6667

If the quotient is a whole number, then 3 and 261,605.6667 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:

1 784,817
-1 -784,817

Let's try dividing by 4:

784,817 ÷ 4 = 196,204.25

If the quotient is a whole number, then 4 and 196,204.25 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:

1 784,817
-1 784,817
Keep dividing by the next highest number until you cannot divide anymore.

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

11171,347784,817
-1-11-71,347-784,817

More Examples

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