77350734400 has 189 divisors, whose sum is σ = 202681236369. Its totient is φ = 29049077760.

The previous prime is 77350734371. The next prime is 77350734401. The reversal of 77350734400 is 443705377.

The square root of 77350734400 is 278120.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in 13 ways, for example, as 1598080576 + 75752653824 = 39976^2 + 275232^2 .

It is a super-2 number, since 2×77350734400² (a number of 23 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (40).

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (77350734401) by changing a digit.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 189121396 + ... + 189121804.

Almost surely, 2^77350734400 is an apocalyptic number.

77350734400 is the 278120-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 77350734400

77350734400 is an abundant number, since it is smaller than the sum of its proper divisors (125330501969).

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

77350734400 is an equidigital number, since it uses as much as digits as its factorization.

77350734400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 874 (or 433 counting only the distinct ones).

The product of its (nonzero) digits is 246960, while the sum is 40.

The spelling of 77350734400 in words is "seventy-seven billion, three hundred fifty million, seven hundred thirty-four thousand, four hundred".