Question

A list consists of the following pairs of numbers:

(i) 51, 53; 55, 57; 59, 61; 63, 65; 67, 69; 71, 73

Categorize them as pairs of:

(i) co-primes
(ii) primes
(iii) composites

Answer 1

(i) Co-primes: Two natural numbers are said to be co-prime numbers if they have 1 as their only common factor.
Hence, all the given pairs of numbers are co-primes.

(ii) Primes: Natural numbers which have exactly two distinct factors, i.e., 1 and the number itself are called prime numbers.
Hence, (59, 61) and (71, 73) are pairs of prime numbers.

(iii) Composite numbers: Natural numbers which have more than two factors are called composite numbers.
Hence, (55, 57) and (63, 65) are pairs of composite numbers.