Question

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

Answer 1

First, Let's Make it clear, What actually a co-prime number is ;

So, two integers x and y are said to be co-prime if the only positive integer that divides both of them is 1.

So, HCF(Highest Common Factor) Should be 1.

So, The Numbers which fulfill the above said conditions are ;

(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

Thanks!

Answer 2

Answer:

factors of 18 are = 1,2,3,6,9, and 18

factors of 35 are = 1,5,7, and 35

therefore 1, is the only commom factor of 18 and 35