Factor pairs of 171 are any two numbers that, when multiplied together, equal 171. The question to ask is “what two numbers multiplied together equal 171?” Every factor can be paired with another factor, and multiplying the two will result in 171.
To find the factor pairs of 171, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 171. 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 3.
Step 2:
Divide 171 by the smallest prime factor, in this case, 3:
171 ÷ 3 = 57
3 and 57 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 57 as the new focus. Find the smallest prime factor that isn’t 1, and divide 57 by that number. In this case, 3 is the new smallest prime factor:
57 ÷ 3 = 19
Remember that this new factor pair is only for the factors of 57, not 171. So, to finish the factor pair for 171, you’d multiply 3 and 3 before pairing with 19:
3 x 3 = 9
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 171:
(1, 171), (3, 57), (9, 19)
So, to list all the factors of 171: 1, 3, 9, 19, 57, 171
The negative factors of 171 would be: -1, -3, -9, -19, -57, -171