HCF of two consecutive numbers is always 1 . explanation : Take two consecutive numbers as 9 and 10. between these two numbers there is no common factor other than 1. Take two consecutive numbers as 17 and 18.

**Explanation:**

To find the HCF (Highest Common Factor) of two consecutive numbers, we need to understand what it means.

The HCF of two numbers is the largest number that divides both of them without leaving any remainder. In other words, it is the greatest common divisor of the two numbers.

Consecutive numbers are those numbers that follow each other in order, with a difference of 1. For example, 3 and 4, 10 and 11, or 100 and 101 are consecutive numbers.

Let's consider two consecutive numbers: x and x+1.

To find the HCF of these numbers, we need to check all the factors of both numbers and see if there is any common factor.

**Factors of x:**
The factors of a number are the numbers that divide it without leaving any remainder.

For example, let's consider the number 6. The factors of 6 are 1, 2, 3, and 6.

So, the factors of x are: 1 and x.

**Factors of x+1:**
Similarly, the factors of x+1 are: 1 and x+1.

Now, let's compare the factors of x and x+1.

The only common factor between x and x+1 is 1. This means that 1 is the only number that divides both x and x+1 without leaving any remainder.

Therefore, the HCF of two consecutive numbers is 1.

Hence, the correct answer is option **B) 1**.

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