22176

22176 is a natural number that lies between 22175 and 22177. It is an even and composite integer, often used in mathematical examples and explorations of number properties.

The prime factorization of 22176 is 2^5 × 3^2 × 7 × 11. This factorization implies a rich divisor structure: 22176 has 72 positive divisors. It is divisible by 2, 4, 8, 16, 32, as well as by 3, 9, 7, and 11, and by many products of these primes. The sum of its decimal digits is 18, so the number is divisible by 9 and 3, and its digital root is 9. Because of this, 22176 is a Harshad (Niven) number in base 10.

In more advanced arithmetic, Euler’s totient function yields φ(22176) = 5760, which counts the integers up to 22176 that are coprime to 22176. Base representations include hexadecimal 0x56A0, octal 0o53240, and binary 0b0101011010100000, reflecting the same value in different numeral systems. The decimal form can also be expressed as 32 × 693, highlighting its factorization.

Overall, 22176 is notable for its composite structure with multiple small prime factors, its status as a Harshad number, and its exact totient, all of which illustrate common themes in elementary number theory.