19656

19656 is a positive integer. In its prime factorization, it equals 2^3 × 3^3 × 7 × 13, which makes it a composite and even number. It has 64 positive divisors, reflecting its multiple prime factors.

Divisibility and numeric properties: Because it contains factors 2^3 and 3^3, 19656 is divisible by 8 and by 27, and hence by 216 (the least common multiple of 8 and 27). Indeed, 19656 = 216 × 91. The sum of its decimal digits is 27, so the number is divisible by 27 and is a Harshad (or Niven) number in base 10. The sum of its proper divisors is 67200 − 19656 = 47544, which exceeds 19656; therefore, 19656 is an abundant number.

Representations in different bases: In decimal, it is 19656. In hexadecimal it is 0x4CC8, since 4 × 4096 + 12 × 256 + 12 × 16 + 8 equals 19656. In binary, 0x4CC8 corresponds to the 16-bit sequence 0100110011001000. In octal, it is 4631, because 4 × 512 + 6 × 64 + 3 × 8 + 1 equals 19656.

Context and usage: As a mathematical integer, 19656 is often cited as an example in factorization, divisor-counting, and base-conversion exercises. Its factorization into 2, 3, 7, and 13 illustrates how composite numbers can combine multiple small primes. Beyond pure mathematics, there is no widely recognized, unique historical or cultural designation attached to the number 19656.