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Question Are the following pairs of numbers co-prime? Guess first and then use prime factorisation to verify your
(a) 30 and 45
(b) 57 and 85
(c) 121 and 1331
(d) 343 and 216
Solution:
(a) 30 and 45
30 = 2 × 3 × 5
45 = 3 × 3 × 5
Clearly, 3 and 5 are the common factors of 30 and 45.
So, these are not co-prime numbers.
(b) 57 and 85
57 = 3 × 19
85 = 5 × 17
Clearly, there is no any common prime factor of 57 and 85.
So, these are co-prime numbers.
(c) 121 and 1331
121 = 11 × n
1331 = 11 × 11 × 11
Clearly, 11 and 11 are the common factors of 121 and 1331.
So, these are not co-prime numbers.
(d) 343 and 216
343 = 7 × 7 × 7
216 = 2 × 2 × 2 × 3 × 3 × 3
Clearly, there is no any common prime factor of 343 and 216.
So, these are co-prime numbers.