20650

20650 is a natural number that sits between 20649 and 20651. In mathematics, it is often cited as an example of a composite integer with a straightforward but nontrivial prime factorization.

Prime factorization and divisors: 20650 = 2 × 5^2 × 7 × 59. This makes the number even and a multiple of 50 (since 5^2 × 2 = 50). Consequently, 20650 has 24 positive divisors, as given by the formula for the number of divisors: (1+1)(2+1)(1+1)(1+1) = 24.

Notable properties: 20650 is not a prime and is not a perfect square. It cannot be expressed as a sum of two squares because its prime factorization includes the primes 7 and 59, both congruent to 3 modulo 4, with odd exponents, which rules out such a representation.

Representations and context: As 413 × 50, with 413 = 7 × 59, the number is an even multiple of 50. In decimal notation, it ends with a 0, indicating divisibility by 10, and specifically by 50.

In summary, 20650 is a structured composite number with a clear factorization and several standard arithmetic properties, often used to illustrate divisor counts and modular considerations in number theory.