Q: What are the factor combinations of the number 65,273?

 A:
Positive:   1 x 6527313 x 5021
Negative: -1 x -65273-13 x -5021


How do I find the factor combinations of the number 65,273?

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 65,273, 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 65,273
-1 -65,273

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 65,273.

Example:
1 x 65,273 = 65,273
and
-1 x -65,273 = 65,273
Notice both answers equal 65,273

With that explanation out of the way, let's continue. Next, we take the number 65,273 and divide it by 2:

65,273 ÷ 2 = 32,636.5

If the quotient is a whole number, then 2 and 32,636.5 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 65,273
-1 -65,273

Now, we try dividing 65,273 by 3:

65,273 ÷ 3 = 21,757.6667

If the quotient is a whole number, then 3 and 21,757.6667 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 65,273
-1 -65,273

Let's try dividing by 4:

65,273 ÷ 4 = 16,318.25

If the quotient is a whole number, then 4 and 16,318.25 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 65,273
-1 65,273
Keep dividing by the next highest number until you cannot divide anymore.

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

1135,02165,273
-1-13-5,021-65,273

More Examples

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