Are the following pairs of numbers co-prime? Guess first and then use prime factorisation to verify your answer. a. 30 and 45 b. 57 and 85 c. 121 and 1331 d. 343 and 216
Are 30 and 45 co-prime?
No, 30 and 45 are not co-prime. They have common prime factors 3 and 5.
Are 57 and 85 co-prime?
Yes, 57 and 85 are co-prime. They have no common prime factor.
Are 121 and 1331 co-prime?
No, 121 and 1331 are not co-prime. They have common prime factor 11.
Are 343 and 216 co-prime?
Yes, 343 and 216 are co-prime. They have no common prime factor.
Explanation
(a) 30 = × 5 and 45 = 3² × 5. Both have 3 and 5 as common prime factors. (b) 57 = and 85 = . There is no common prime factor between them. (c) 121 = 11² and 1331 = 11³. Both have 11 as a common prime factor. (d) 343 = 7³ and 216 = 2³ × 3³. There is no common prime factor between them.