The second question on the Greatest Common Factor Exercise states
"Numbers are said to be “co-prime” if they share no common factors other than 1. Which three numbers below are all co-prime with each other?
Select three answer choices.
- 75
- 100
- 143
- 147
- 154
I, then, found the factors for each number.
75: 1, 3, 5, 15, 25, 75
100: 1, 2, 4, 5, 10, 20, 25, 50, 100
143: 1, 11, 13, 143
147: 1, 3, 7, 21, 49, 147
154: 1, 2, 7, 11, 14, 22, 77, 154
To be co-prime they must share no factors other than one, thus, I chose the numbers, 75, 143 and 154.
However, the solution was stated as "The quickest way to solve this problem would be to notice that both 75 and 100 end with 5 or 0, which means that they must share 5 as a common factor and hence cannot be co-prime. However, we also need to spot that 75 and 147 share 3 as a common factor, which rules this pair out as well. Additionally, 100 and 154 share 2 as a common factor. This results in the correct triplet of 100, 143 and 147.
It is important to note that just because two integers p and q are not co-prime with each other, that does not imply that p and r cannot be co-prime. "
Is there a factor pairing I missed? Is my answer valid? I don’t know where I might have gone wrong. Any help is appreciated, thank you!!