72770400 has 180 divisors, whose sum is σ = 265615812. Its totient is φ = 19388160.

The previous prime is 72770389. The next prime is 72770407. The reversal of 72770400 is 407727.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (180).

It is a super-2 number, since 2×72770400² = 10591062232320000, which contains 22 as substring.

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (72770407) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 29 ways as a sum of consecutive naturals, for example, 64239 + ... + 65361.

Almost surely, 2^72770400 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 72770400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (132807906).

72770400 is an abundant number, since it is smaller than the sum of its proper divisors (192845412).

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

72770400 is a wasteful number, since it uses less digits than its factorization.

72770400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1155 (or 1133 counting only the distinct ones).

The product of its (nonzero) digits is 2744, while the sum is 27.

The square root of 72770400 is about 8530.5568399724. The cubic root of 72770400 is about 417.4952967785.

The spelling of 72770400 in words is "seventy-two million, seven hundred seventy thousand, four hundred".