Q: What are the factor combinations of the number 386,837?

 A:
Positive:   1 x 38683711 x 3516723 x 16819121 x 3197139 x 2783253 x 1529
Negative: -1 x -386837-11 x -35167-23 x -16819-121 x -3197-139 x -2783-253 x -1529


How do I find the factor combinations of the number 386,837?

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 386,837, 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.

1 386,837
-1 -386,837

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 386,837.

Example:
1 x 386,837 = 386,837
and
-1 x -386,837 = 386,837
Notice both answers equal 386,837

With that explanation out of the way, let's continue. Next, we take the number 386,837 and divide it by 2:

386,837 ÷ 2 = 193,418.5

If the quotient is a whole number, then 2 and 193,418.5 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:

1 386,837
-1 -386,837

Now, we try dividing 386,837 by 3:

386,837 ÷ 3 = 128,945.6667

If the quotient is a whole number, then 3 and 128,945.6667 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:

1 386,837
-1 -386,837

Let's try dividing by 4:

386,837 ÷ 4 = 96,709.25

If the quotient is a whole number, then 4 and 96,709.25 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:

1 386,837
-1 386,837
Keep dividing by the next highest number until you cannot divide anymore.

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

111231211392531,5292,7833,19716,81935,167386,837
-1-11-23-121-139-253-1,529-2,783-3,197-16,819-35,167-386,837

More Examples

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