Q: What are the factor combinations of the number 767,717?

 A:
Positive:   1 x 76771723 x 3337929 x 26473667 x 1151
Negative: -1 x -767717-23 x -33379-29 x -26473-667 x -1151


How do I find the factor combinations of the number 767,717?

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 767,717, 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.

1 767,717
-1 -767,717

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 767,717.

Example:
1 x 767,717 = 767,717
and
-1 x -767,717 = 767,717
Notice both answers equal 767,717

With that explanation out of the way, let's continue. Next, we take the number 767,717 and divide it by 2:

767,717 ÷ 2 = 383,858.5

If the quotient is a whole number, then 2 and 383,858.5 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:

1 767,717
-1 -767,717

Now, we try dividing 767,717 by 3:

767,717 ÷ 3 = 255,905.6667

If the quotient is a whole number, then 3 and 255,905.6667 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:

1 767,717
-1 -767,717

Let's try dividing by 4:

767,717 ÷ 4 = 191,929.25

If the quotient is a whole number, then 4 and 191,929.25 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:

1 767,717
-1 767,717
Keep dividing by the next highest number until you cannot divide anymore.

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

123296671,15126,47333,379767,717
-1-23-29-667-1,151-26,473-33,379-767,717

More Examples

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