NCERT Exercise 3.6 solution class six math
Question (1) Find the HCF of the following numbers:
(a) 18, 48
Solution
The prime factors of 18 = 2 × 3 × 3
The prime factors of 48 = 2 × 2 × 2 × 2 × 3
Thus, the HCF of 18 and 48 = 2 × 3 = 6 Answer
(b) 30, 42
Solution
The prime factors of 30 = 2 × 3 × 5
The prime factors of 42 = 2 × 3 × 7
Thus, the HCF of 30 and 42 = 2 × 3 = 6 Answer
(c) 18, 60
Solution
The prime factors of 18 = 2 × 3 × 3
The prime factors of 60 = 2 × 2 × 3 × 5
Thus, the HCF of 18 and 60 = 2 × 3 = 6 Answer
(d) 27, 63
Solution
The prime factors of 27 = 3 × 3 × 3
The prime factors of 63 = 3 × 3 × 7
Thus, the HCF of 27 and 63 = 3 × 3 = 9 Answer
(e) 36, 84
Solution
The prime factors of 36 = 2 × 2 × 3 × 3
The prime factors of 84 = 2 × 2 × 3 × 7
Thus, the HCF of 18 and 48 = 2 × 2 × 3 = 12 Answer
(f) 34, 102
Solution
The prime factors of 34 = 2 × 17
The prime factors of 102 = 2 × 3 × 17
Thus, the HCF of 18 and 48 = 2 × 17 = 34 Answer
(g) 70, 105, 175
Solution
The prime factors of 70 = 2 × 5 × 7
The prime factors of 105 = 3 × 5 × 7
The prime factors of 175 = 5 × 5 × 7
Thus, the HCF of 70, 105 and 175 = 5 × 7 = 35 Answer
Question (2) What is the HCF of two consecutive
(a) numbers?
Answer
The HCF of two consecutive numbers = 1
Example (a)
HCF of 5 and 6
The prime factor of 5 = 5
The prime factor of 6 = 2 × 3
Now since no common factors present between 5 and 6, thus the HCF = 1
Example (b)
HCF of 14 and 15
The prime factor of 14 = 2 × 7
The prime factor of 15 = 3 × 5
Now since no common factors present between 14 and 15, thus the HCF = 1
What is the HCF to two consecutive (b) even numbers?
Answer
The HCF of two consecutive even numbers = 2 Answer
Example (a)
HCF of two consecutive even numbers 6 and 8
The prime factors of 6 = 2 × 3
The prime factors of 8 = 2 × 2 × 2
Thus, HCF of 6 and 8 = 2 Answer
Example (b)
HCF of two consecutive even numbers 28 and 30
The prime factors of 28 = 2 × 2 × 7
The prime factors of 30 = 2 × 3 × 5
Thus, HCF of 28 and 30 = 2 Answer
What is the HCF to two consecutive (c) Odd numbers?
Answer
The HCF of two consecutive odd numbers = 1 Answer
Example (a)
HCF of two consecutive odd numbers 5 and 7
The prime factors of 4 = 5 (Because 5 is a prime number)
The prime factors of 7 = 7 (Because 7 is a prime number)
Now since there is no common factor between 4 and 7, thus the HCF of 4 and 7 = 1 Answer
Example (b)
HCF of two consecutive odd numbers 25 and 27
The prime factors of 25 = 5 × 5
The prime factors of 27 = 3 × 3 × 3
Now since there is no common factor between 25 and 27, thus the HCF of 25 and 27 = 1 Answer
Question (3) HCF of co-prime numbers 4 and 15 was found as follows by factorisation:
4 = 2 × 2 and 15 = 3 × 5 since there is no common prime factor, so HCF of 4 and 15 is 0. Is the answer correct? If not, what is the correct HCF
Answer
If there is no common prime factor between two number, then the HCF of such two numbers = 1
Thus, the given answer 0 in not correct.
The HCF of given numbers = 1 Answer