156250

156250 is a composite number that appears in various mathematical contexts, particularly within number theory and combinatorics. It can be expressed as the product of its prime factors: 2 × 5³ × 7⁴. This decomposition highlights its divisibility by small primes, making it a useful number in certain algebraic and arithmetic studies.

In combinatorics, 156250 holds significance as the number of possible ways to partition a set of 10 distinct elements into subsets of sizes 1, 2, 3, and 4, following the multinomial coefficient formula. Specifically, it equals 10!/(1! × 2! × 3! × 4!), reflecting its role in counting problems involving grouped arrangements.

The number also appears in the context of the Bell numbers, which enumerate the number of partitions of a set of *n* elements. While not a Bell number itself, 156250 is closely related to the 10th Bell number (115975) and the 11th Bell number (567293), appearing in related combinatorial expansions.

Additionally, 156250 is notable in recreational mathematics as part of sequences involving powers of primes. Its structure, derived from the exponents of its prime factors, makes it an interesting case study in number theory, particularly in the analysis of highly composite numbers—those with more divisors than any smaller positive integer.

While 156250 lacks widespread recognition in everyday contexts, its mathematical properties contribute to its relevance in specialized fields, including cryptography, coding theory, and algorithmic design, where divisibility and factorization play critical roles.