51800 has 48 divisors (see below), whose sum is σ = 141360. Its totient is φ = 17280.

The previous prime is 51797. The next prime is 51803. The reversal of 51800 is 815.

51800 = 83² + 84² + ... + 89².

It is an interprime number because it is at equal distance from previous prime (51797) and next prime (51803).

It is a Harshad number since it is a multiple of its sum of digits (14).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (51803) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 1382 + ... + 1418.

It is an arithmetic number, because the mean of its divisors is an integer number (2945).

2⁵¹⁸⁰⁰ is an apocalyptic number.

51800 is a gapful number since it is divisible by the number (50) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 51800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (70680).

51800 is an abundant number, since it is smaller than the sum of its proper divisors (89560).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

51800 is a wasteful number, since it uses less digits than its factorization.

51800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 60 (or 51 counting only the distinct ones).

The product of its (nonzero) digits is 40, while the sum is 14.

The square root of 51800 is about 227.5961335348. The cubic root of 51800 is about 37.2771973800.

The spelling of 51800 in words is "fifty-one thousand, eight hundred".