77306112 has 216 divisors, whose sum is σ = 251105400. Its totient is φ = 22708224.

The previous prime is 77306087. The next prime is 77306129. The reversal of 77306112 is 21160377.

It can be written as a sum of positive squares in 4 ways, for example, as 147456 + 77158656 = 384^2 + 8784^2 .

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 868564 + ... + 868652.

It is an arithmetic number, because the mean of its divisors is an integer number (1162525).

Almost surely, 2^77306112 is an apocalyptic number.

77306112 is a gapful number since it is divisible by the number (72) 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 77306112, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (125552700).

77306112 is an abundant number, since it is smaller than the sum of its proper divisors (173799288).

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

77306112 is a wasteful number, since it uses less digits than its factorization.

77306112 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 153 (or 136 counting only the distinct ones).

The product of its (nonzero) digits is 1764, while the sum is 27.

The square root of 77306112 is about 8792.3894363250. The cubic root of 77306112 is about 425.9951067348.

Adding to 77306112 its reverse (21160377), we get a palindrome (98466489).

The spelling of 77306112 in words is "seventy-seven million, three hundred six thousand, one hundred twelve".