3968

3968 is a natural number that follows 3967 and precedes 3969. It is an even composite number with prime factorization 2^7 × 31, since 3968 = 128 × 31.

Because of its factorization, 3968 has 16 positive divisors: 1, 2, 4, 8, 16, 32, 64, 128, 31, 62, 124, 248, 496, 992, 1984, and 3968. It is divisible by powers of two up to 2^7 and by 31, reflecting its mixed prime structure.

In common base representations, 3968 can be written as:

- Binary: 1111100000000_2

- Hexadecimal: 0xF80

- Octal: 0o7600

From a number-theory standpoint, 3968 equals 2^12 − 2^7, or equivalently 31 × 128. This makes it a product of a Mersenne prime (31 = 2^5 − 1) and a power of two, a form that occasionally appears in discussions of factorization patterns and binary arithmetic.

Beyond these basic properties, 3968 does not have a widely noted special role in mathematics or culture. It serves primarily as an example of a moderately large composite number with a simple prime factorization and standard representations in multiple bases.