15750

15750 is a natural number that follows 15749 and precedes 15751. It is an even, composite number with a factorization that reveals its small prime components. The prime factorization is 15750 = 2 × 3^2 × 5^3 × 7, which implies a total of 48 positive divisors.

Divisibility and digit properties: The sum of its digits is 18, so 15750 is divisible by 9 and by 3, and consequently by 18. Because it contains factors of 2 and 5, it is also divisible by 10, as well as by 14, 25, 50, 125, and 250. In base 10 it is a Harshad (Niven) number since it is divisible by the sum of its digits (18).

Sum of divisors and abundance: The divisor-sum function gives sigma(15750) = 48,672, meaning the sum of its proper divisors is 32,922. Since this is greater than 15750, the number is abundant.

Base representations: In hexadecimal, 15750 is 0x3D86. In binary, using a 16-bit form, it is 0011110110000110.

Applications and interpretation: The factorization 2 × 3^2 × 5^3 × 7 makes 15750 a useful example in number theory for illustrating divisor counts, Harshad properties, and the relationship between prime exponents and the sum-of-divisors function. Its divisibility by several small powers of 2 and 5 reflects its composition and its role in arithmetic exercises.