Q: What are the factor combinations of the number 412,889?

 A:
Positive:   1 x 41288919 x 2173131 x 13319589 x 701
Negative: -1 x -412889-19 x -21731-31 x -13319-589 x -701


How do I find the factor combinations of the number 412,889?

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 412,889, 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.

1 412,889
-1 -412,889

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 412,889.

Example:
1 x 412,889 = 412,889
and
-1 x -412,889 = 412,889
Notice both answers equal 412,889

With that explanation out of the way, let's continue. Next, we take the number 412,889 and divide it by 2:

412,889 ÷ 2 = 206,444.5

If the quotient is a whole number, then 2 and 206,444.5 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:

1 412,889
-1 -412,889

Now, we try dividing 412,889 by 3:

412,889 ÷ 3 = 137,629.6667

If the quotient is a whole number, then 3 and 137,629.6667 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:

1 412,889
-1 -412,889

Let's try dividing by 4:

412,889 ÷ 4 = 103,222.25

If the quotient is a whole number, then 4 and 103,222.25 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:

1 412,889
-1 412,889
Keep dividing by the next highest number until you cannot divide anymore.

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

1193158970113,31921,731412,889
-1-19-31-589-701-13,319-21,731-412,889

More Examples

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