Factor pairs of 82 are any two numbers that, when multiplied together, equal 82. The question to ask is “what two numbers multiplied together equal 82?” Every factor can be paired with another factor, and multiplying the two will result in 82.
To find the factor pairs of 82, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 82. For reference, the first prime numbers to check are 2, 3, 5, 7, 11, and 13. In this case, the smallest factor that’s a prime number larger than 1 is 2.
Step 2:
Divide 82 by the smallest prime factor, in this case, 2:
82 ÷ 2 = 41
2 and 41 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 41 as the new focus. Find the smallest prime factor that isn’t 1, and divide 41 by that number. In this case, 41 is the new smallest prime factor:
41 ÷ 41 = 1
Remember that this new factor pair is only for the factors of 41, not 82. So, to finish the factor pair for 82, you’d multiply 2 and 41 before pairing with 1:
2 x 41 = 82
Step 4:
Repeat this process until there are no longer any prime factors larger than one to divide by. At the end, you should have the full list of factor pairs.
Here are all the factor pairs for 82:
(1, 82), (2, 41)
So, to list all the factors of 82: 1, 2, 41, 82
The negative factors of 82 would be: -1, -2, -41, -82