Question

Which of the following pair of number are co-prime?
a) 30,415
b) 17,69
c) 16,81
d) 15,100​

Answer 1

Answer:

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

Answer 2

The pair of numbers which are co-primes are (b) 17, 69  and (c) 16,81.

Explanation:

• Those numbers which have only 1 as the highest common factor or just a common factor are called co-prime numbers.
• In this question,

       ⇒ Factors of  $415=1, 5, 83, 415.$

       ⇒ Factors of  $30=1,2,3,5,6,10,15,30$

• Hence, they both have $1\ and\ 5$ as common factors out of which 5 is the HCF. therefore option (a) is not the correct option.

      ⇒ Factors of $17=1,17$

      ⇒ Factors of $69=1,3,23,69$

• They do not have any factor in common except 1 which makes it the HCF. Therefore, option (b) is correct.

     ⇒Factors of $16=1,2,4,8,16$

     ⇒Factors of $81=1,3,9,27,81$

• Hence, They too do not have any common factor except 1. Therefore, option (c) is also correct.

    ⇒Factors of $15=1,3,5,15$

    ⇒Factors of $100=1,2,4,5,10,20,25,50,100$

• Hence, they both have $1\ and\ 5$ as common factors which makes 5 as the HCF. Therefore option (d) is incorrect.