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Question

# 1. What is the HCF of two consecutive(a) Numbers?(b) Even numbers?(c) Odd numbers?2. Find the HCF of the following :8 and 12

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Solution

## 1. (a) Let's take any two consecutive numbers as 4 and 5.There is no common factor other than 1 between 4 and 5. Similarly, if we take any other two consecutive numbers, HCF will be 1, only, as they are not having any common factor other than 1.Hence, HCF of two consecutive numbers will be 1.(b) Let's take any two consecutive even numbers as 6 and 8.Prime factorization of 6 and 86=2×38=2×2×2HCF of 6 and 8 is 2.Similarly, if we take any other two consecutive even numbers, HCF will be 2 only, as they are multiple of 2.Hence, HCF of two consecutive even numbers will be 2.(c) Let's take any two consecutive odd numbers as 9 and 11.Prime factorization of 9 and 119=3×311=11HCF of 9 and 11 is 1.Similarly, if we take any other two consecutive odd numbers, HCF will be 1 only, as they are not having any common factor other than 1.Hence, HCF of two consecutive odd numbers will be 1. 2. Lets find prime factorization of 8 and 12,8=2×2×212=2×2×3HCF of 8 and 12=2×2=4Hence, HCF of 4 and 12 is 4.

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