72800 has 72 divisors (see below), whose sum is σ = 218736. Its totient is φ = 23040.

The previous prime is 72797. The next prime is 72817. The reversal of 72800 is 827.

72800 = T₂₇ + T₂₈ + ... + T₇₆.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 5594 + ... + 5606.

It is an arithmetic number, because the mean of its divisors is an integer number (3038).

2⁷²⁸⁰⁰ is an apocalyptic number.

72800 is a gapful number since it is divisible by the number (70) 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 72800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (109368).

72800 is an abundant number, since it is smaller than the sum of its proper divisors (145936).

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

72800 is a wasteful number, since it uses less digits than its factorization.

72800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 40 (or 27 counting only the distinct ones).

The product of its (nonzero) digits is 112, while the sum is 17.

The square root of 72800 is about 269.8147512646. The cubic root of 72800 is about 41.7551895733.

It can be divided in two parts, 72 and 800, that multiplied together give a square (57600 = 240²).

The spelling of 72800 in words is "seventy-two thousand, eight hundred".