151840

151840 is a number that appears in various contexts across mathematics, computing, and popular culture, often due to its unique properties and appearances in notable sequences. It is a composite number, meaning it has divisors other than one and itself. Specifically, 151840 can be factored into primes as 2^6 × 3^3 × 5 × 7, reflecting its divisibility by many integers.

In combinatorics, 151840 holds significance as the number of possible permutations of the letters in the word "supercalifragilisticexpialidocious," a term famously popularized by the 1964 film *Mary Poppins*. This word, with 34 letters, has 151840 distinct arrangements, making it a notable example in studies of permutations and anagrams.

The number also appears in the context of the factorial of 7, denoted as 7!, which equals 5040, and the factorial of 8, 8! = 40320. However, 151840 is more directly linked to the number of possible ways to arrange 10 distinct items, which is 10! = 3,628,800, but it is also a term in the sequence of factorials multiplied by other constants in certain combinatorial problems.

In computing, 151840 has been referenced in programming challenges and puzzles, often as a benchmark or target value for algorithms involving permutations or factorials. Its appearance in such contexts stems from its role in illustrating computational complexity and efficiency in generating or evaluating large sets of combinations.

While not widely recognized in everyday use, 151840 serves as an interesting case study in mathematics and recreational number theory, demonstrating how seemingly arbitrary numbers can emerge in meaningful ways across different fields.