Question

Which of the following numbers are co prime:
1. 30 and 415
2. 17 and 68
3. 216 and 215
4. 81 and 16
Please step by step explain like
Factor of 30 =?
Factor of 415=?
Common factor=?
Since they are co prime

Answer 1

Answer:

Co-prime:

Two numbers having only 1 as a common factor are called co- prime numbers. Two consecutive prime numbers are co-prime. Two prime numbers are always co-prime but co-prime numbers need not always be Prime.

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Solution:

(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 15 = 1, 3, 5, 15

Factors of 37 = 1, 37

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.

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

(f) Factors of 81 = 1, 3, 9, 27, 81

Factors of 16 = 1, 2, 4, 8, 16

Common factor = 1

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

----------------------------------------------------------------------------------------------------Hence (a) , (b) , (e) & (f) are co-prime.-------------------------------------------------------------------------------------------------Hope this will help you......