196

196 is a natural number that follows 195 and precedes 197. It is even and composite, and it is the square of 14, making it a perfect square (14^2). Its prime factorization is 2^2 × 7^2, and its divisors are 1, 2, 4, 7, 14, 28, 49, 98, and 196. As the 14th square number, it has nine divisors, and its sum of divisors is 399. In various bases, 196 is represented as follows: binary 11000100, octal 304, decimal 196, hexadecimal C4; in other bases it is 21021 in base 3, 1241 in base 5, 400 in base 7, and 237 in base 9. In Roman numerals, 196 is written as CXCVI.

196 is notable in recreational number theory for the so-called 196 problem, which asks whether 196 is a happy number under the process of repeatedly replacing a number by the sum of the squares of its digits. Starting from 196, the sequence goes 196 → 118 → 66 → 72 → 53 → 34 → 25 → 29 → 85 → 89 → 145 → 42 → 20 → 4 → 16 → 37 → 58 → 89, which enters the known cycle 89 → 145 → 42 → 20 → 4 → 16 → 37 → 58 → 89. This demonstrates that 196 is not a happy number.

Historically, 196 can be read as a calendar year (196 CE/AD) and was a leap year in the Julian calendar. The number’s Roman numeral form is CXCVI, reflecting its place in classical numbering systems.