Q: What are the factor combinations of the number 845,746?

 A:
Positive:   1 x 8457462 x 42287311 x 7688622 x 3844337 x 2285874 x 11429407 x 2078814 x 1039
Negative: -1 x -845746-2 x -422873-11 x -76886-22 x -38443-37 x -22858-74 x -11429-407 x -2078-814 x -1039


How do I find the factor combinations of the number 845,746?

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 845,746, 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.

1 845,746
-1 -845,746

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 845,746.

Example:
1 x 845,746 = 845,746
and
-1 x -845,746 = 845,746
Notice both answers equal 845,746

With that explanation out of the way, let's continue. Next, we take the number 845,746 and divide it by 2:

845,746 ÷ 2 = 422,873

If the quotient is a whole number, then 2 and 422,873 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 422,873 845,746
-1 -2 -422,873 -845,746

Now, we try dividing 845,746 by 3:

845,746 ÷ 3 = 281,915.3333

If the quotient is a whole number, then 3 and 281,915.3333 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 2 422,873 845,746
-1 -2 -422,873 -845,746

Let's try dividing by 4:

845,746 ÷ 4 = 211,436.5

If the quotient is a whole number, then 4 and 211,436.5 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 2 422,873 845,746
-1 -2 -422,873 845,746
Keep dividing by the next highest number until you cannot divide anymore.

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

12112237744078141,0392,07811,42922,85838,44376,886422,873845,746
-1-2-11-22-37-74-407-814-1,039-2,078-11,429-22,858-38,443-76,886-422,873-845,746

More Examples

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