Q: What are the factor combinations of the number 4,133?

 A:
Positive:   1 x 4133
Negative: -1 x -4133


How do I find the factor combinations of the number 4,133?

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 4,133, 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 4,133
-1 -4,133

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 4,133.

Example:
1 x 4,133 = 4,133
and
-1 x -4,133 = 4,133
Notice both answers equal 4,133

With that explanation out of the way, let's continue. Next, we take the number 4,133 and divide it by 2:

4,133 ÷ 2 = 2,066.5

If the quotient is a whole number, then 2 and 2,066.5 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 4,133
-1 -4,133

Now, we try dividing 4,133 by 3:

4,133 ÷ 3 = 1,377.6667

If the quotient is a whole number, then 3 and 1,377.6667 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 4,133
-1 -4,133

Let's try dividing by 4:

4,133 ÷ 4 = 1,033.25

If the quotient is a whole number, then 4 and 1,033.25 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 4,133
-1 4,133
Keep dividing by the next highest number until you cannot divide anymore.

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

14,133
-1-4,133

More Examples

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