Find the highest common factor (HCF) of the two numbers 865 and 2595.

Introduction:
This is a basic question on the highest common factor (HCF) of two numbers. It is designed to test whether you can recognise when one number is an exact multiple of another and hence immediately see the HCF.

Given Data / Assumptions:

• Two numbers: 865 and 2595
• We are asked to find their HCF.

Concept / Approach:
The HCF of two numbers is the largest positive integer that divides both numbers without leaving any remainder. If one number divides the other exactly, then the smaller number itself is the HCF. We can check divisibility either by simple multiplication or by the Euclidean algorithm.

Step-by-Step Solution:
Check whether 2595 is a multiple of 865. Compute 865 × 3 = 2595 Since 2595 equals 865 × 3 exactly, 865 divides 2595 without remainder. Therefore, any common factor of 865 and 2595 must also be a factor of 865. The largest such factor is clearly 865 itself. So HCF(865, 2595) = 865

Verification / Alternative check:
Using the Euclidean algorithm: divide 2595 by 865. The quotient is 3 and the remainder is 0. When the remainder becomes 0, the divisor at that step is the HCF. Here that divisor is 865, confirming the answer.

Why Other Options Are Wrong:
5 and 25 are factors of both numbers but they are not the highest common factor. 2595 cannot be the HCF because it is greater than 865 and obviously does not divide 865. Therefore only 865 satisfies the requirement of being the greatest common divisor.

Common Pitfalls:
Students sometimes choose a small common factor like 5 or 25 because they do not check whether one number is an exact multiple of the other. Always look for the possibility that the smaller number might divide the larger number completely, which immediately gives you the HCF.

Final Answer:
The highest common factor of 865 and 2595 is 865.