Question

Which of the following pairs are co-prime? i 18 and 35 ii. 216 and 215 ii . 30 and 415 iv. 17 and 68 ​

Answer 1

Which of the following pairs are co-prime?

i. 18 and 35

ii. 216 and 215iii. 30 and 415

iv. 17 and 68

(a) Factors of 18 = 1, 2, 3, 6, 9, 18

Factors of 35 = 1, 5, 7, 35

Common factor = 1

Since, both the numbers have only one common factor, i.e., 1, therefore, they are co-prime number.

(b) Factors of 216 = 1, 2, 3, 4, 6, 8, 36, 72, 108, 216

Factors of 215 = 1, 5, 43, 215

Common factor = 1

Since, both the numbers have only one common factor, i.e., 1, therefore, they are co-prime number.

(c) Factors of 30 = 1, 2, 3, 5, 6, 15, 30

Factors of 415 = 1, 5, …….., 83, 415

Common factor = 1, 5

Since, both the numbers have more than one common factor, therefore, they are not co-prime number.

(d) Factors of 17 = 1, 17

Factors of 68 = 1, 2, 4, 17, 34, 86

Common factor = 1, 17

Since, both the numbers have more than one common factor, therefore, they are not co-prime number.

So, (a) and (b) are the required answer