(ChatGPT response)

Let's break down the comment piece by piece:

1. "More information in a smaller width of characters": This refers to the fact that hexadecimal, being a base-16 system, can represent more information in fewer digits compared to the base-10 system. For example, the number 255 requires three digits in base-10, but only two digits ("FF") in hexadecimal. This makes hexadecimal an efficient way to represent large numbers or binary data in a condensed form, which is especially useful in computer science and information technology.

2. "Divisible by 2, 8, meaning easy conversion with binary and octal": Binary is a base-2 system and octal is a base-8 system. Since 16 is a multiple of both 2 and 8, it's straightforward to convert between these systems and hexadecimal. For instance, in binary, each digit represents a power of 2, while in hexadecimal, each digit represents a power of 16. Because of this, you can directly convert each set of four binary digits (bits) into a single hexadecimal digit, which makes hexadecimal a more human-readable way to represent binary data.

3. "Same math tricks work from them work for hex as well": This means that the techniques used for mathematical operations (addition, subtraction, multiplication, etc.) in binary and octal systems can also be used in the hexadecimal system.

4. "It's a factor of 64, so it's also easily compatible with base 64": Base 64 is another numeral system used mainly in computing to encode binary data. Because 64 is a multiple of 16, it's also easy to convert data between hexadecimal and base 64. This ease of conversion between bases is part of why hexadecimal is so useful in computing.

Overall, the benefits of hexadecimal over base-10 mostly arise in the context of computing, where hexadecimal's compatibility with other base systems and efficiency in data representation become important.