3972

3972 is a natural number that sits between 3971 and 3973. It is even and composite. The prime factorization of 3972 is 2^2 × 3 × 331, which yields a set of positive divisors {1, 2, 3, 4, 6, 12, 331, 662, 993, 1324, 1986, 3972}. Consequently, the number of positive divisors is 12. The radical of 3972, the product of its distinct prime factors, is rad(3972) = 2 × 3 × 331 = 1986, and the sum of its positive divisors is σ(3972) = 9296.

In various numeral systems, 3972 has the representations 111110000100 in binary, 7604 in octal, and 0xF84 in hexadecimal. In Roman numerals, it is written as MMMCMLXXII. The number is divisible by 4 (the last two digits form 72, which is divisible by 4) and by 3 (the sum of digits, 3+9+7+2 = 21, is divisible by 3); it is therefore divisible by 12 as well (since 12 = 4 × 3). It is not divisible by 5 or 7, and its prime factorization confirms its composite status.

No widely recognized mathematical constant or famous theorem is specifically associated with the number 3972. As with most integers, it participates in various arithmetic and algebraic contexts, including divisor-related functions, modular arithmetic, and base-conversion representations.