466560

466,560 is a positive integer. Its prime factorization is 2^7 × 3^6 × 5, which can also be written as 6^6 × 10 or as 640 × 729. This shows the number is highly composite in terms of having many small prime factors, and it is divisible by 10 and by 128, with the exact factorization indicating 2^7 and 3^6 in its makeup.

The number has 112 positive divisors, calculated as (7+1)(6+1)(1+1) = 8 × 7 × 2. The sum of its divisors is 1,672,290, obtained from the multiplicative property of the sigma function: (2^8−1)/(2−1) × (3^7−1)/(3−1) × (5^2−1)/(5−1) = 255 × 1093 × 6. In decimal terms, the digit sum is 27, which confirms divisibility by 9; combined with divisibility by 5, the number is a multiple of 45.

A convenient representation is 466,560 = 640 × 729, highlighting its decomposition into 2^7 × 5 and 3^6. It is also equal to 6^6 × 10, since 6^6 = 46,656. These forms illustrate how the number emerges from powers of small primes and a simple factor of 10.

Applications of 466,560 generally arise in mathematical discussions involving divisor structure, factorial-related counts, or as a illustrative example of a number with a large number of divisors relative to its size.

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