Question

What is the HCF of two consecutive numbers?

Answer 1

Answer:

The Highest Common Factor (HCF) of two or more numbers is the greatest factor that divides the two given numbers.

HCF of two consecutive numbers

The HCF of two consecutive numbers is always one. The reason behind this is that the two consecutive numbers do not have any common factor other than 1. Hence 1 becomes the HCF between two consecutive numbers.

• HCF of two consecutive integers is 1
• HCF of two consecutive even integers is 1
• HCF of two consecutive odd integers is 1
• HCF of two co-primes is equal to 1

Example:

Let us take two consecutive numbers 5 and 6.

The two numbers have 1 as a common factor and nothing else.

Hence 1 is the HCF.

This proves that the HCF of any two consecutive numbers is always a one.

Articles to Explore:

1. Find the LCM and HCF of the following integers by applying the prime factorization method. (1)12, 15 and 21 (2)17, 23 and 29 (3)8, 9 and 25
2. Find HCF of 867 and 225 by Euclid’s division algorithm.