77338400 has 72 divisors (see below), whose sum is σ = 190026900. Its totient is φ = 30735360.

The previous prime is 77338363. The next prime is 77338409. The reversal of 77338400 is 483377.

It can be written as a sum of positive squares in 6 ways, for example, as 23697424 + 53640976 = 4868^2 + 7324^2 .

It is a super-2 number, since 2×77338400² = 11962456229120000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (32).

It is not an unprimeable number, because it can be changed into a prime (77338409) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 221426 + ... + 221774.

Almost surely, 2^77338400 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 77338400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (95013450).

77338400 is an abundant number, since it is smaller than the sum of its proper divisors (112688500).

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

77338400 is a wasteful number, since it uses less digits than its factorization.

77338400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 646 (or 633 counting only the distinct ones).

The product of its (nonzero) digits is 14112, while the sum is 32.

The square root of 77338400 is about 8794.2253780535. The cubic root of 77338400 is about 426.0544061234.

The spelling of 77338400 in words is "seventy-seven million, three hundred thirty-eight thousand, four hundred".