Q: What are the factor combinations of the number 41,167?

 A:
Positive:   1 x 411677 x 5881
Negative: -1 x -41167-7 x -5881


How do I find the factor combinations of the number 41,167?

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 41,167, 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 41,167
-1 -41,167

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 41,167.

Example:
1 x 41,167 = 41,167
and
-1 x -41,167 = 41,167
Notice both answers equal 41,167

With that explanation out of the way, let's continue. Next, we take the number 41,167 and divide it by 2:

41,167 ÷ 2 = 20,583.5

If the quotient is a whole number, then 2 and 20,583.5 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 41,167
-1 -41,167

Now, we try dividing 41,167 by 3:

41,167 ÷ 3 = 13,722.3333

If the quotient is a whole number, then 3 and 13,722.3333 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 41,167
-1 -41,167

Let's try dividing by 4:

41,167 ÷ 4 = 10,291.75

If the quotient is a whole number, then 4 and 10,291.75 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 41,167
-1 41,167
Keep dividing by the next highest number until you cannot divide anymore.

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

175,88141,167
-1-7-5,881-41,167

More Examples

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