To find the highest common factor (HCF) of 65/117, we need to find the largest number that can divide both 65 and 117 without leaving a remainder.

First, let’s find the prime factors of 65 and 117:

65 = 5 * 13 117 = 3 * 3 * 13

Now, let’s compare the prime factors of both numbers:

The prime factors of 65 are 5 and 13. The prime factors of 117 are 3, 3, and 13.

The common prime factors are 13.

Therefore, the HCF of 65/117 is 13.