Q: What are the factor combinations of the number 772,123?

 A:
Positive:   1 x 77212311 x 7019317 x 45419187 x 4129
Negative: -1 x -772123-11 x -70193-17 x -45419-187 x -4129


How do I find the factor combinations of the number 772,123?

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 772,123, 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.

1 772,123
-1 -772,123

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 772,123.

Example:
1 x 772,123 = 772,123
and
-1 x -772,123 = 772,123
Notice both answers equal 772,123

With that explanation out of the way, let's continue. Next, we take the number 772,123 and divide it by 2:

772,123 ÷ 2 = 386,061.5

If the quotient is a whole number, then 2 and 386,061.5 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:

1 772,123
-1 -772,123

Now, we try dividing 772,123 by 3:

772,123 ÷ 3 = 257,374.3333

If the quotient is a whole number, then 3 and 257,374.3333 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:

1 772,123
-1 -772,123

Let's try dividing by 4:

772,123 ÷ 4 = 193,030.75

If the quotient is a whole number, then 4 and 193,030.75 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:

1 772,123
-1 772,123
Keep dividing by the next highest number until you cannot divide anymore.

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

111171874,12945,41970,193772,123
-1-11-17-187-4,129-45,419-70,193-772,123

More Examples

Here are some more numbers to try:

Try the factor calculator

Explore more about the number 772,123:


Ask a Question