Question

Find the HCF of
(i) two prime numbers
(ii) two consecutive numbers
(iii) two co-primes
(iv) 2 and an even number

Answer 1

(i) 2 and 3 are two prime numbers.
Now, HCF of 2 and 3 is as follows:
2 = 2 × 1
3 = 3 × 1
∴ HCF = 1

(ii) 4 and 5 are two consecutive numbers.
Now, HCF of 4 and 5 is as follows:
4 = 2 × 2 × 1 = 2² × 1
5 = 5 × 1
∴ HCF = 1

(iii) 2 and 3 are two co-primes.
Now, HCF of 2 and 3 is as follows:
2 = 2 × 1
3 = 3 × 1
∴ HCF = 1

(iv) 2 and 4 are two even numbers.
Now, HCF of 2 and 4 is as follows:​
2 = 2 × 1
4 = 2 × 2 × 1
∴ HCF = 2 × 1 = 2