Q: What are the factor combinations of the number 78,671?

 A:
Positive:   1 x 78671151 x 521
Negative: -1 x -78671-151 x -521


How do I find the factor combinations of the number 78,671?

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 78,671, 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 78,671
-1 -78,671

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 78,671.

Example:
1 x 78,671 = 78,671
and
-1 x -78,671 = 78,671
Notice both answers equal 78,671

With that explanation out of the way, let's continue. Next, we take the number 78,671 and divide it by 2:

78,671 ÷ 2 = 39,335.5

If the quotient is a whole number, then 2 and 39,335.5 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 78,671
-1 -78,671

Now, we try dividing 78,671 by 3:

78,671 ÷ 3 = 26,223.6667

If the quotient is a whole number, then 3 and 26,223.6667 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 78,671
-1 -78,671

Let's try dividing by 4:

78,671 ÷ 4 = 19,667.75

If the quotient is a whole number, then 4 and 19,667.75 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 78,671
-1 78,671
Keep dividing by the next highest number until you cannot divide anymore.

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

115152178,671
-1-151-521-78,671

More Examples

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