Factor pairs of 174 are any two numbers that, when multiplied together, equal 174. The question to ask is “what two numbers multiplied together equal 174?” Every factor can be paired with another factor, and multiplying the two will result in 174.
To find the factor pairs of 174, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 174. 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 174 by the smallest prime factor, in this case, 2:
174 ÷ 2 = 87
2 and 87 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 87 as the new focus. Find the smallest prime factor that isn’t 1, and divide 87 by that number. In this case, 3 is the new smallest prime factor:
87 ÷ 3 = 29
Remember that this new factor pair is only for the factors of 87, not 174. So, to finish the factor pair for 174, you’d multiply 2 and 3 before pairing with 29:
2 x 3 = 6
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 174:
(1, 174), (2, 87), (3, 58), (6, 29)
So, to list all the factors of 174: 1, 2, 3, 6, 29, 58, 87, 174
The negative factors of 174 would be: -1, -2, -3, -6, -29, -58, -87, -174