Question

Which of the following numbers are co-prime: (a) 18 and 35 (b) 15 and 37 (c) 30 and 415 (d) 17 and 168 (e) 216 and 215 (f) 81 and 16

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Answer 1

SOLUTION :-

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

Factors of 35 = 1, 5, 7, 35

Common factor =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 = 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 = 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 = 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 =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 = 1

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

Answer 2

Co-prime are numbers that do not share any common factors except 1

Question (a);

Prime factors of 18 = 2 x 3²

Prime factors of 35 = 5 x 7

HCF = 1

Answer: Yes, they are co-prime

Question (b);

Prime factors of 15 = 3 x 5

Prime factors of 37 = 37

HCF = 1

Answer: Yes, they are co-prime

Question (c);

Prime factors of 30 = 2 x 3 x 5

Prime factors of 415 = 5 x 83

HCF = 5

Answer: No, they are not co-prime

Question (d);

Prime factors of 17 = 17

Prime factors of 68 = 2² x 17

HCF = 17

Answer: No, they are not co-prime

Question (e);

Prime factors of 216 = 2³ x 3³

Prime factors of 215 = 5 x 43

HCF = 1

Answer: Yes, they are co-prime

Question (f);

Prime factors of 81 = 3⁴

Prime factors of 16 = 2⁴

HCF = 1

Answer: Yes, they are co-prime