34800 has 60 divisors (see below), whose sum is σ = 115320. Its totient is φ = 8960.

The previous prime is 34781. The next prime is 34807. The reversal of 34800 is 843.

34800 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

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

It is a super-2 number, since 2×34800² = 2422080000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (15).

It is a plaindrome in base 13.

It is a self number, because there is not a number n which added to its sum of digits gives 34800.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (34807) 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, 1186 + ... + 1214.

It is an arithmetic number, because the mean of its divisors is an integer number (1922).

2³⁴⁸⁰⁰ is an apocalyptic number.

34800 is a gapful number since it is divisible by the number (30) 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 34800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (57660).

34800 is an abundant number, since it is smaller than the sum of its proper divisors (80520).

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

34800 is a wasteful number, since it uses less digits than its factorization.

34800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 50 (or 39 counting only the distinct ones).

The product of its (nonzero) digits is 96, while the sum is 15.

The square root of 34800 is about 186.5475810618. The cubic root of 34800 is about 32.6482380206.

It can be divided in two parts, 3 and 4800, that multiplied together give a square (14400 = 120²).

The spelling of 34800 in words is "thirty-four thousand, eight hundred".