Q: What are the factor combinations of the number 60,709?

 A:
Positive:   1 x 6070911 x 5519
Negative: -1 x -60709-11 x -5519


How do I find the factor combinations of the number 60,709?

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 60,709, 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 60,709
-1 -60,709

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 60,709.

Example:
1 x 60,709 = 60,709
and
-1 x -60,709 = 60,709
Notice both answers equal 60,709

With that explanation out of the way, let's continue. Next, we take the number 60,709 and divide it by 2:

60,709 ÷ 2 = 30,354.5

If the quotient is a whole number, then 2 and 30,354.5 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 60,709
-1 -60,709

Now, we try dividing 60,709 by 3:

60,709 ÷ 3 = 20,236.3333

If the quotient is a whole number, then 3 and 20,236.3333 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 60,709
-1 -60,709

Let's try dividing by 4:

60,709 ÷ 4 = 15,177.25

If the quotient is a whole number, then 4 and 15,177.25 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 60,709
-1 60,709
Keep dividing by the next highest number until you cannot divide anymore.

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

1115,51960,709
-1-11-5,519-60,709

More Examples

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