77212800 has 288 divisors, whose sum is σ = 315694080. Its totient is φ = 17602560.

The previous prime is 77212781. The next prime is 77212813. The reversal of 77212800 is 821277.

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 201409 + ... + 201791.

It is an arithmetic number, because the mean of its divisors is an integer number (1096160).

Almost surely, 2^77212800 is an apocalyptic number.

77212800 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 77212800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (157847040).

77212800 is an abundant number, since it is smaller than the sum of its proper divisors (238481280).

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

77212800 is a wasteful number, since it uses less digits than its factorization.

77212800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 420 (or 400 counting only the distinct ones).

The product of its (nonzero) digits is 1568, while the sum is 27.

The square root of 77212800 is about 8787.0814267309. The cubic root of 77212800 is about 425.8236392245.

The spelling of 77212800 in words is "seventy-seven million, two hundred twelve thousand, eight hundred".