13050

13050 is a natural number that follows 13049 and precedes 13051. In mathematical terms, it is an even composite number with a rich prime factorization and several notable divisibility properties.

Its prime factorization is 2 × 3^2 × 5^2 × 29, giving it 36 positive divisors in total. The prime factors are 2, 3, 5 and 29. Because it ends in zero, it is divisible by 10, and consequently by many of its smaller divisors as well.

13050 has several interesting number-theoretic characteristics. It is a Harshad (or Niven) number in base 10, since the sum of its digits is 1 + 3 + 0 + 5 + 0 = 9 and 13050 is divisible by 9 (13050 ÷ 9 = 1450). It is also a practical number, meaning that every smaller positive integer can be expressed as a sum of distinct divisors of 13050. This property holds because, for its prime factorization in ascending order (2, 3, 5, 29 with exponents 1, 2, 2, 1), each subsequent prime satisfies the standard practicality criterion: p1 = 2, p2 ≤ 1 + σ(2^1) = 4, p3 ≤ 1 + σ(2^1 3^2) = 40, and p4 ≤ 1 + σ(2^1 3^2 5^2) = 1210, which 29 satisfies.

In summary, 13050 is a composite, even integer with a 36-divisor structure, and it exhibits both Harshad and practical number properties, reflecting its layered factorization 2 × 3^2 × 5^2 × 29.