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Which of the following numbers are co-prime? (a) 18 and 35 (b) 15 and 37 (c) 30 and 415 (d) 17 and 68 (e) 216 and 215 (f) 81 and 16
Solution:
A Co-prime number is a set of numbers or integers which have only 1 as their common factor i.e. their highest common factor (HCF) will be 1.
(a)
Factors of 18 = 1, 2, 3, 6, 9,18
Factors of 35 = 1, 5, 7, 35
Common factor of 18 and 35 = 1
Since both have only one common factor, i.e., 1, therefore, they are co-prime numbers.
(b)
Factors of 15 = 1, 3, 5,15
Factors of 37 = 1, 37
Common factor of 15 and 37 = 1
since both have only one common factor, i.e., 1, therefore, they are co-prime numbers.
(c)
Factors of 30 = 1, 2, 3, 5, 6, 15, 30
Factors of 415 = 1, 5, 83, 415
Common factor of 30 and 415 = 1,5
Since both have more than one common factor, therefore, they are not co-prime numbers
(d)
Factors of 17 = 1, 17
Factors of 68 = 1, 2, 4, 17, 34, 86
Common factor of 17 and 68 = 1, 17
Since, both have more than one common factor, therefore, they are not co-prime numbers
(e)
Factors of 216 = 1, 2, 3, 4, 6, 8, 36, 72, 108,216
Factors of 215 = 1, 5, 43, 215
Common factor of 216 and 215 = 1
Since, both Have only one common factor, i.e , 1 , therefore they are co-prime numbers.
(f)
Factors of 81 = 1, 3, 9, 27, 81
Factors of 16 = 1, 2, 4, 8, 16
Common factor of 81 and 16 = 1
Since both have only one common factor, i.e., 1, therefore, they are co-prime numbers.