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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:

We will be using the concept of co-prime numbers to solve this.

(a) Given numbers are 18 and 35

Factors of 18 are 1, 2, 3, 6, 9, 18
Factors of 35 are 1, 5, 7, 35
The common factor of 18 and 35 is only 1.
Therefore, 18 and 35 are co-prime.

(b) Given numbers are 15 and 37

Factors of 15 are 1, 3, 5, 15
Factors of 37 are 1, 37
The common factor of 15 and 37 is only 1.
Therefore, 15 and 37 are co-prime.

(c) Given numbers are 30 and 415

Factors of 30 are 1, 2, 3, 5, 6, 15, 30
Factors of 415 are 1, 5, 83, 415
The common factors of 30 and 415 are 1 and 5.
Therefore, 30 and 415 are not co-prime.

(d) Given numbers are 17 and 68
Factors of 17 are 1, 17
Factors of 68 are 1, 2, 4, 17, 34, 68
The common factors of 17 and 68 are 1 and 17.
Therefore, 17 and 68 are not co-prime.

(e) Given numbers are 216 and 215
Factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
Factors of 215 are 1, 5, 43, 215
The common factor of 216 and 215 is only 1.
Therefore, 216 and 215 are co-prime.

(f) Given numbers are 81 and 16
Factors of 81 are 1, 3, 9, 27, 81
Factors of 16 are 1, 2, 4, 8, 16
The common factor of 81 and 16 is only 1.
Therefore, they are co-prime.

You can also use the co-prime calculator to check this.

NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.4 Question 5

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

Summary:

The co-prime numbers are (a) 18 and 35 (b) 15 and 37 (e) 216 and 215 and (f) 81 and 16

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