Which of the following are pairs of coprimes? i. 8,14 ii. 4,5 iii.

1.	Which of the following are pairs of coprimes? 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 coprimes? 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.