Q: What are the factor combinations of the number 65,503?

 A:
Positive:   1 x 6550331 x 2113
Negative: -1 x -65503-31 x -2113


How do I find the factor combinations of the number 65,503?

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 65,503, 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 65,503
-1 -65,503

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 65,503.

Example:
1 x 65,503 = 65,503
and
-1 x -65,503 = 65,503
Notice both answers equal 65,503

With that explanation out of the way, let's continue. Next, we take the number 65,503 and divide it by 2:

65,503 ÷ 2 = 32,751.5

If the quotient is a whole number, then 2 and 32,751.5 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 65,503
-1 -65,503

Now, we try dividing 65,503 by 3:

65,503 ÷ 3 = 21,834.3333

If the quotient is a whole number, then 3 and 21,834.3333 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 65,503
-1 -65,503

Let's try dividing by 4:

65,503 ÷ 4 = 16,375.75

If the quotient is a whole number, then 4 and 16,375.75 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 65,503
-1 65,503
Keep dividing by the next highest number until you cannot divide anymore.

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

1312,11365,503
-1-31-2,113-65,503

More Examples

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