7648

7648 is a natural number that follows 7647 and precedes 7649. It is an even, composite number with a prime factorization of 7648 = 2^5 × 239, meaning the highest power of two dividing it is 32 and the remaining odd factor is the prime 239.

The positive divisors of 7648 are 1, 2, 4, 8, 16, 32, 239, 478, 956, 1912, 3824, and 7648. Consequently, the number of positive divisors is (5+1)(1+1) = 12. The sum of all divisors is sigma(7648) = 63 × 240 = 15120, so the sum of proper divisors is 15120 − 7648 = 7472. Since 7472 < 7648, 7648 is a deficient number, with a deficiency of 7648 − 7472 = 176.

In common numeral bases, 7648 is represented as 0x1DE0 in hexadecimal and as 0o16740 in octal. In binary, it has a 13-bit representation with the prime factorization indicating its 2-adic valuation of 5 (divisible by 32 but not by 64).

Beyond these arithmetic properties, there is no widely noted mathematical constant or notable cultural reference uniquely tied to the number 7648. It primarily appears in contexts where exact numeric values are needed, similar to other large even composite integers.