77105609760400 has 135 divisors (see below), whose sum is σ = 200598008373489. Its totient is φ = 28468920629760.

The previous prime is 77105609760337. The next prime is 77105609760409. The reversal of 77105609760400 is 406790650177.

The square root of 77105609760400 is 8780980.

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 68037224347024 + 9068385413376 = 8248468^2 + 3011376^2 .

It is a Harshad number since it is a multiple of its sum of digits (52).

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (77105609760409) 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, 2283037914 + ... + 2283071686.

Almost surely, 2^{77105609760400} is an apocalyptic number.

77105609760400 is the 8780980-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 77105609760400

77105609760400 is an abundant number, since it is smaller than the sum of its proper divisors (123492398613089).

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

77105609760400 is an frugal number, since it uses more digits than its factorization.

77105609760400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 67590 (or 33793 counting only the distinct ones).

The product of its (nonzero) digits is 2222640, while the sum is 52.

The spelling of 77105609760400 in words is "seventy-seven trillion, one hundred five billion, six hundred nine million, seven hundred sixty thousand, four hundred".