46800 has 90 divisors (see below), whose sum is σ = 174902. Its totient is φ = 11520.

The previous prime is 46771. The next prime is 46807. The reversal of 46800 is 864.

46800 is digitally balanced in base 2 and base 4, because in such bases it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in 3 ways, for example, as 144 + 46656 = 12^2 + 216^2 .

It is a tau number, because it is divible by the number of its divisors (90).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a nialpdrome in base 15.

It is a zygodrome in base 15.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (46807) by changing a digit.

46800 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 3594 + ... + 3606.

2⁴⁶⁸⁰⁰ is an apocalyptic number.

46800 is a gapful number since it is divisible by the number (40) 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 46800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (87451).

46800 is an abundant number, since it is smaller than the sum of its proper divisors (128102).

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

46800 is a wasteful number, since it uses less digits than its factorization.

46800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 37 (or 23 counting only the distinct ones).

The product of its (nonzero) digits is 192, while the sum is 18.

The square root of 46800 is about 216.3330765278. Note that the first 3 decimals coincide. The cubic root of 46800 is about 36.0369989983.

The spelling of 46800 in words is "forty-six thousand, eight hundred".