3200

3200 is a natural number that follows 3199 and precedes 3201. It is an even, composite integer with a prime factorization of 2^7 × 5^2, which implies it is divisible by many integers, including 2, 4, 5, 10, and 100.

In number theory, 3200 has 24 positive divisors. The sum of all divisors equals 7905, so the sum of its proper divisors is 4705, making 3200 an abundant number. It is also a Harshad (Niven) number in base 10, since 3200 is divisible by the sum of its digits (3 + 2 + 0 + 0 = 5).

In other numeral systems, 3200 is represented as 110010000000 in binary, 0x0C80 in hexadecimal, and 0o6200 in octal. In Roman numerals, it is written as MMMCC.

Historically, around 3200 BCE writing is believed to have emerged in Mesopotamia, with early cuneiform tablets dating to roughly 3200–3000 BCE. This period marks the transition toward record-keeping and literacy in the region, often associated with the Uruk culture and the development of urbanization.

In summary, 3200 is a versatile reference in mathematics and a historically notable date range for the origins of writing, while also serving as a common example of base-conversion and number-theory properties.