51600 has 60 divisors (see below), whose sum is σ = 169136. Its totient is φ = 13440.

The previous prime is 51599. The next prime is 51607. The reversal of 51600 is 615.

51600 is nontrivially palindromic in base 7.

It is a tau number, because it is divible by the number of its divisors (60).

It is a Harshad number since it is a multiple of its sum of digits (12).

It is a nialpdrome in base 16.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 51600.

It is not an unprimeable number, because it can be changed into a prime (51607) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 1179 + ... + 1221.

2⁵¹⁶⁰⁰ is an apocalyptic number.

51600 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 51600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (84568).

51600 is an abundant number, since it is smaller than the sum of its proper divisors (117536).

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

51600 is a wasteful number, since it uses less digits than its factorization.

51600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 64 (or 53 counting only the distinct ones).

The product of its (nonzero) digits is 30, while the sum is 12.

The square root of 51600 is about 227.1563338320. The cubic root of 51600 is about 37.2291597013.

It can be divided in two parts, 5 and 1600, that multiplied together give a cube (8000 = 20³).

The spelling of 51600 in words is "fifty-one thousand, six hundred".