Q: What are the factor combinations of the number 30,077?

 A:
Positive:   1 x 3007719 x 1583
Negative: -1 x -30077-19 x -1583


How do I find the factor combinations of the number 30,077?

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 30,077, 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 30,077
-1 -30,077

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 30,077.

Example:
1 x 30,077 = 30,077
and
-1 x -30,077 = 30,077
Notice both answers equal 30,077

With that explanation out of the way, let's continue. Next, we take the number 30,077 and divide it by 2:

30,077 ÷ 2 = 15,038.5

If the quotient is a whole number, then 2 and 15,038.5 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 30,077
-1 -30,077

Now, we try dividing 30,077 by 3:

30,077 ÷ 3 = 10,025.6667

If the quotient is a whole number, then 3 and 10,025.6667 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 30,077
-1 -30,077

Let's try dividing by 4:

30,077 ÷ 4 = 7,519.25

If the quotient is a whole number, then 4 and 7,519.25 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 30,077
-1 30,077
Keep dividing by the next highest number until you cannot divide anymore.

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

1191,58330,077
-1-19-1,583-30,077

More Examples

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