What is the HCF of two consecutive numbers?

The Highest Common Factor (HCF) of two consecutive numbers is always 1. This is because consecutive numbers differ by 1, meaning they have no other common factors besides 1.

Understanding Consecutive Numbers

Consecutive numbers are integers that follow one another in order. For example, 4 and 5, or 10 and 11 are pairs of consecutive numbers.

Why is the HCF 1?

• Consecutive numbers have no shared divisors other than 1.
• For instance, the factors of 4 are 1, 2, and 4, while the factors of 5 are 1 and 5.

Examples

Let’s look at a couple of examples:

• For 7 and 8: The factors are 1, 7 for 7 and 1, 2, 4, 8 for 8. The only common factor is 1.
• For 14 and 15: The factors are 1, 2, 7, 14 for 14 and 1, 3, 5, 15 for 15. Again, the only common factor is 1.

In summary, the HCF of any two consecutive numbers is always 1, as they share no other common factors. This property holds true for all pairs of consecutive integers.