Q: What are the factor combinations of the number 42,067?

 A:
Positive:   1 x 4206723 x 182931 x 135759 x 713
Negative: -1 x -42067-23 x -1829-31 x -1357-59 x -713


How do I find the factor combinations of the number 42,067?

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 42,067, 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 42,067
-1 -42,067

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 42,067.

Example:
1 x 42,067 = 42,067
and
-1 x -42,067 = 42,067
Notice both answers equal 42,067

With that explanation out of the way, let's continue. Next, we take the number 42,067 and divide it by 2:

42,067 ÷ 2 = 21,033.5

If the quotient is a whole number, then 2 and 21,033.5 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 42,067
-1 -42,067

Now, we try dividing 42,067 by 3:

42,067 ÷ 3 = 14,022.3333

If the quotient is a whole number, then 3 and 14,022.3333 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 42,067
-1 -42,067

Let's try dividing by 4:

42,067 ÷ 4 = 10,516.75

If the quotient is a whole number, then 4 and 10,516.75 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 42,067
-1 42,067
Keep dividing by the next highest number until you cannot divide anymore.

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

12331597131,3571,82942,067
-1-23-31-59-713-1,357-1,829-42,067

More Examples

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