Q: What are the factor combinations of the number 845,123?

 A:
Positive:   1 x 845123419 x 2017
Negative: -1 x -845123-419 x -2017


How do I find the factor combinations of the number 845,123?

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 845,123, 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.

1 845,123
-1 -845,123

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 845,123.

Example:
1 x 845,123 = 845,123
and
-1 x -845,123 = 845,123
Notice both answers equal 845,123

With that explanation out of the way, let's continue. Next, we take the number 845,123 and divide it by 2:

845,123 ÷ 2 = 422,561.5

If the quotient is a whole number, then 2 and 422,561.5 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:

1 845,123
-1 -845,123

Now, we try dividing 845,123 by 3:

845,123 ÷ 3 = 281,707.6667

If the quotient is a whole number, then 3 and 281,707.6667 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:

1 845,123
-1 -845,123

Let's try dividing by 4:

845,123 ÷ 4 = 211,280.75

If the quotient is a whole number, then 4 and 211,280.75 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:

1 845,123
-1 845,123
Keep dividing by the next highest number until you cannot divide anymore.

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

14192,017845,123
-1-419-2,017-845,123

More Examples

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