77506813440 has 1120 divisors, whose sum is σ = 338125233600. Its totient is φ = 16625958912.

The previous prime is 77506813429. The next prime is 77506813463. The reversal of 77506813440 is 4431860577.

77506813440 is a `hidden beast` number, since 7 + 7 + 506 + 8 + 134 + 4 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1120).

It is a super-2 number, since 2×77506813440² (a number of 23 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 111 ways as a sum of consecutive naturals, for example, 222082386 + ... + 222082734.

It is an arithmetic number, because the mean of its divisors is an integer number (301897530).

Almost surely, 2^77506813440 is an apocalyptic number.

77506813440 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 77506813440, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (169062616800).

77506813440 is an abundant number, since it is smaller than the sum of its proper divisors (260618420160).

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

77506813440 is an equidigital number, since it uses as much as digits as its factorization.

77506813440 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 414 (or 383 counting only the distinct ones).

The product of its (nonzero) digits is 564480, while the sum is 45.

The spelling of 77506813440 in words is "seventy-seven billion, five hundred six million, eight hundred thirteen thousand, four hundred forty".