Which of the following are pairs of co-primes? i. 8, 14 ii. 4, 5 i

1.	Which of the following are pairs of co-primes? i. 8, 14 ii. 4, 5 iii. 17, 19 iv. 27, 15
Answer» i. Factors of 8: 1, 2, 4, 8 Factors of 14: 1, 2, 7, 14 ∴ Common factors of 8 and 14: 1, 2 ∴ 8 and 14 are not a pair of co-prime numbers. ii. Factors of 4: 1, 4 Factors of 5 : 1, 5 ∴ Common factors of 4 and 5 : 1 ∴ 4 and 5 are a pair of co-prime numbers. iii. Factors of 17 : 1, 17 Factors of 19 : 1, 19 ∴ Common factors of 17 and 19 : 1 ∴ 17 and 19 are a pair of co-prime numbers. iv. Factors of 27: 1, 3, 9, 27 Factors of 15: 1, 3, 5, 15. ∴ Common factors of 27 and 15 : 1, 3 ∴ 27 and 15 are not a pair of co-prime numbers.

Which of the following are pairs of co-primes? i. 8, 14 ii. 4, 5 iii. 17, 19 iv. 27, 15

Answer»

i. Factors of 8: 1, 2, 4, 8

Factors of 14: 1, 2, 7, 14

∴ Common factors of 8 and 14: 1, 2

∴ 8 and 14 are not a pair of co-prime numbers.

ii. Factors of 4: 1, 4

Factors of 5 : 1, 5

∴ Common factors of 4 and 5 : 1

∴ 4 and 5 are a pair of co-prime numbers.

iii. Factors of 17 : 1, 17

Factors of 19 : 1, 19

∴ Common factors of 17 and 19 : 1

∴ 17 and 19 are a pair of co-prime numbers.

iv. Factors of 27: 1, 3, 9, 27

Factors of 15: 1, 3, 5, 15.

∴ Common factors of 27 and 15 : 1, 3

∴ 27 and 15 are not a pair of co-prime numbers.