Q: What are the factor combinations of the number 396,773?

 A:
Positive:   1 x 39677313 x 3052123 x 17251299 x 1327
Negative: -1 x -396773-13 x -30521-23 x -17251-299 x -1327


How do I find the factor combinations of the number 396,773?

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 396,773, 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.

1 396,773
-1 -396,773

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 396,773.

Example:
1 x 396,773 = 396,773
and
-1 x -396,773 = 396,773
Notice both answers equal 396,773

With that explanation out of the way, let's continue. Next, we take the number 396,773 and divide it by 2:

396,773 ÷ 2 = 198,386.5

If the quotient is a whole number, then 2 and 198,386.5 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:

1 396,773
-1 -396,773

Now, we try dividing 396,773 by 3:

396,773 ÷ 3 = 132,257.6667

If the quotient is a whole number, then 3 and 132,257.6667 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:

1 396,773
-1 -396,773

Let's try dividing by 4:

396,773 ÷ 4 = 99,193.25

If the quotient is a whole number, then 4 and 99,193.25 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:

1 396,773
-1 396,773
Keep dividing by the next highest number until you cannot divide anymore.

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

113232991,32717,25130,521396,773
-1-13-23-299-1,327-17,251-30,521-396,773

More Examples

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