Chapter 3 Playing With Numbers Ex. 3.6
Question 1.
Find the HCF of the following numbers:
(a) 18, 48
(b) 30, 42
(c) 18, 60
(d) 27,63
(e) 36,84
(f) 34, 102
(g) 70, 105, 175
(h) 91, 112, 49
(i) 18, 54, 81
(j) 12, 45, 75
Solution:
Question 2.
What is the HCF of two consecutive
(a) numbers?
(b) even numbers?
(c) odd numbers?
Solution:
(a) The common factor of two consecutive numbers is always 1.
Hence, the HCF = 1.
(b) The common factors of two consecutive even numbers are 1 and 2.
Hence, the HCF = 1 x 2 = 2.
(c) The common factor of two consecutive odd numbers is 1.
Hence, the HCF = 1.
Question 3.
HCF of co-prime numbers 4 and 15 was found as follows by factorisation:
4 = 2 x 2 and 15 = 3 x 15. Since there is no common prime factors, so HCF of 4 and 15 is 0.
Is the answer correct? If not, what is the correct HCF?
Solution:
No, answer is not correct.
Reason: 0 is not the prime factor of any number.
1 is always the prime factor of co-prime number.
Hence, the correct HCF of 4 and 15 is 1.