Question

11. Categorise the given pairs as co-prime or twin
primes.
(a) (41, 43) (b) (45, 47) (c) (49, 51)
(d) (51, 53) (e) (55, 57) (f) (63, 65)
(g) (67, 69) (h) (71, 73)​

Answer 1

Topic :-

Number System

Given :-

(a) (41, 43) (b) (45, 47) (c) (49, 51)  (d) (51, 53) (e) (55, 57) (f) (63, 65)  (g) (67, 69) (h) (71, 73)

Question :-

Categorise the given pairs as co-prime or twin  primes.

Solution :-

Co-prime Numbers

Two natural numbers (not necessarily prime) are co-prime, if their H.C.F. is 1.

Twin Prime Numbers

If the difference between two prime numbers is two, then the numbers are twin prime numbers.

Checking given pairs,

(a) (41, 43)

43 - 41 = 2

41 and 43 are prime numbers.

41 and 43 have H.C.F. = 1

Hence, this pair is Co-prime as well as Twin Prime too.

(b) (45, 47)

47 - 45 = 2 but

45 is not a prime number.

45 and 47 have H.C.F. = 1

Hence, this pair is Co-Prime.

(c) (49, 51)

51 - 49 = 2 but

49 and 51 are not prime numbers.

49 and 51 have H.C.F. = 1

Hence, this pair is Co-Prime.

(d) (51, 53)

53 - 51 = 2 but

51 is not a prime number.

51 and 53 have H.C.F. = 1

Hence, this pair is Co-prime.

(e) (55, 57)

57 - 55 = 2 but

55 and 57 are not prime numbers.

55 and 57 have H.C.F. = 1

Hence, this pair is Co-Prime.

(f) (63, 65)

65 - 63 = 2 but

63 and 65 are not prime numbers.

63 and 65 have H.C.F. = 1

Hence, this pair is Co-Prime.

(g) (67, 69)

69 - 67 = 2 but

69 is not a prime number.

67 and 69 have H.C.F. = 1

Hence, this pair is Co-Prime.

(h) (71, 73)

73 - 71 = 2

71 and 73 are prime numbers.

71 and 73 have H.C.F. = 1

Hence, this pair is Co-prime as well as Twin Prime too.

Answer :-

Co-prime as well as Twin-Prime :- (a) and (h)

Co-Prime :- (b), (c), (d), (e), (f) and (g)