Q: What are the factor combinations of the number 33,869?

 A:
Positive:   1 x 3386911 x 3079
Negative: -1 x -33869-11 x -3079


How do I find the factor combinations of the number 33,869?

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 33,869, 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 33,869
-1 -33,869

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 33,869.

Example:
1 x 33,869 = 33,869
and
-1 x -33,869 = 33,869
Notice both answers equal 33,869

With that explanation out of the way, let's continue. Next, we take the number 33,869 and divide it by 2:

33,869 ÷ 2 = 16,934.5

If the quotient is a whole number, then 2 and 16,934.5 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 33,869
-1 -33,869

Now, we try dividing 33,869 by 3:

33,869 ÷ 3 = 11,289.6667

If the quotient is a whole number, then 3 and 11,289.6667 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 33,869
-1 -33,869

Let's try dividing by 4:

33,869 ÷ 4 = 8,467.25

If the quotient is a whole number, then 4 and 8,467.25 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 33,869
-1 33,869
Keep dividing by the next highest number until you cannot divide anymore.

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

1113,07933,869
-1-11-3,079-33,869

More Examples

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