What is the HCF of Two Consecutive Numbers?

The Highest Common Factor (HCF), also known as the greatest common divisor (GCD), of two numbers is the largest positive integer that perfectly divides both numbers without leaving a remainder. In other words, it is the greatest number that both numbers can be divided by exactly.

Answer: The Highest Common Factor (HCF) of two consecutive numbers is always 1.

Consecutive numbers are integers that follow one another in sequence, with a difference of 1 between them. For instance, 5 and 6, 12 and 13, or 99 and 100 are consecutive numbers. When calculating the HCF of two consecutive numbers, it’s important to understand that they share no common factors other than 1, because consecutive numbers are only divisible by 1 and themselves.

To illustrate, consider two consecutive numbers, “n” and “n+1.” If we attempt to find their HCF, we realize that the only positive integer that divides both of them is 1. Any other factor would mean that they are not truly consecutive.

Hence, the HCF of two consecutive numbers is invariably 1 due to the absence of common factors other than 1, making them unique in terms of divisibility.