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    Exercise 6.3.6

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6th class > > Exercise 6.3.6

Exercise 6.3.6

  1. Find the HCF of the following numbers?

a. 18,48 = x = 6

b. 30,42 = x = 6

c. 18,60 = x = 6

d. 27,63 = x = 9

2.What is the HCF of two consecutive (a) numbers?(b) even numbers?(c) odd numbers?
a.Numbers-Since consecutive numbers differ by 1, they have no common factors other than 1.
Example- Factors of 4 and 5 are 1,, ,5 common factors are 1
b.Even Numbers-Two consecutive even numbers can be represented as 2n and 2n+2 where n is a integer.
Example- Factors of 4 and 6 are 1, 2,, , , 10 The only common factor between any two consecutive even numbers is 2.
c.Two consecutive odd numbers can be represented as 2n+1 and 2n+3 where n is an integer.
Example- Factors of 3 and 5 are 1,, Consecutive odd numbers are always odd and differ by 2. Since they are consecutive, they have no common factors other than 1.
  1. 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.

Since and have no common prime factors, they are . The correct HCF of two co-prime numbers is always , not 0.

Conclusion: The correct HCF of 4 and 15 is 1