Q: What are the factor combinations of the number 777,749?

 A:
Positive:   1 x 7777497 x 111107137 x 5677811 x 959
Negative: -1 x -777749-7 x -111107-137 x -5677-811 x -959


How do I find the factor combinations of the number 777,749?

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 777,749, 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.

1 777,749
-1 -777,749

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 777,749.

Example:
1 x 777,749 = 777,749
and
-1 x -777,749 = 777,749
Notice both answers equal 777,749

With that explanation out of the way, let's continue. Next, we take the number 777,749 and divide it by 2:

777,749 ÷ 2 = 388,874.5

If the quotient is a whole number, then 2 and 388,874.5 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:

1 777,749
-1 -777,749

Now, we try dividing 777,749 by 3:

777,749 ÷ 3 = 259,249.6667

If the quotient is a whole number, then 3 and 259,249.6667 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:

1 777,749
-1 -777,749

Let's try dividing by 4:

777,749 ÷ 4 = 194,437.25

If the quotient is a whole number, then 4 and 194,437.25 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:

1 777,749
-1 777,749
Keep dividing by the next highest number until you cannot divide anymore.

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

171378119595,677111,107777,749
-1-7-137-811-959-5,677-111,107-777,749

More Examples

Here are some more numbers to try:

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