72424800 has 288 divisors, whose sum is σ = 299980800. Its totient is φ = 16519680.

The previous prime is 72424787. The next prime is 72424817. The reversal of 72424800 is 842427.

It is a tau number, because it is divible by the number of its divisors (288).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 150961 + ... + 151439.

It is an arithmetic number, because the mean of its divisors is an integer number (1041600).

Almost surely, 2^72424800 is an apocalyptic number.

72424800 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 72424800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (149990400).

72424800 is an abundant number, since it is smaller than the sum of its proper divisors (227556000).

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

72424800 is a wasteful number, since it uses less digits than its factorization.

72424800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 515 (or 496 counting only the distinct ones).

The product of its (nonzero) digits is 3584, while the sum is 27.

The square root of 72424800 is about 8510.2761412307. The cubic root of 72424800 is about 416.8333271072.

The spelling of 72424800 in words is "seventy-two million, four hundred twenty-four thousand, eight hundred".