Q: What are the factor combinations of the number 51,089?

 A:
Positive:   1 x 5108947 x 1087
Negative: -1 x -51089-47 x -1087


How do I find the factor combinations of the number 51,089?

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 51,089, 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 51,089
-1 -51,089

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 51,089.

Example:
1 x 51,089 = 51,089
and
-1 x -51,089 = 51,089
Notice both answers equal 51,089

With that explanation out of the way, let's continue. Next, we take the number 51,089 and divide it by 2:

51,089 ÷ 2 = 25,544.5

If the quotient is a whole number, then 2 and 25,544.5 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 51,089
-1 -51,089

Now, we try dividing 51,089 by 3:

51,089 ÷ 3 = 17,029.6667

If the quotient is a whole number, then 3 and 17,029.6667 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 51,089
-1 -51,089

Let's try dividing by 4:

51,089 ÷ 4 = 12,772.25

If the quotient is a whole number, then 4 and 12,772.25 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 51,089
-1 51,089
Keep dividing by the next highest number until you cannot divide anymore.

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

1471,08751,089
-1-47-1,087-51,089

More Examples

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