772072000 has 224 divisors, whose sum is σ = 2316577536. Its totient is φ = 248832000.

The previous prime is 772071991. The next prime is 772072003. The reversal of 772072000 is 270277.

It is a tau number, because it is divible by the number of its divisors (224).

It is a Harshad number since it is a multiple of its sum of digits (25).

It is not an unprimeable number, because it can be changed into a prime (772072003) by changing a digit.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 951595 + ... + 952405.

It is an arithmetic number, because the mean of its divisors is an integer number (10341864).

Almost surely, 2^772072000 is an apocalyptic number.

772072000 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 772072000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1158288768).

772072000 is an abundant number, since it is smaller than the sum of its proper divisors (1544505536).

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

772072000 is a wasteful number, since it uses less digits than its factorization.

772072000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 862 (or 842 counting only the distinct ones).

The product of its (nonzero) digits is 1372, while the sum is 25.

The square root of 772072000 is about 27786.1836170425. The cubic root of 772072000 is about 917.3870407156.

The spelling of 772072000 in words is "seven hundred seventy-two million, seventy-two thousand".