77112000 has 560 divisors, whose sum is σ = 345204288. Its totient is φ = 16588800.

The previous prime is 77111999. The next prime is 77112001. The reversal of 77112000 is 21177.

It is an interprime number because it is at equal distance from previous prime (77111999) and next prime (77112001).

It is a tau number, because it is divible by the number of its divisors (560).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is not an unprimeable number, because it can be changed into a prime (77112001) by changing a digit.

It is a polite number, since it can be written in 79 ways as a sum of consecutive naturals, for example, 4535992 + ... + 4536008.

Almost surely, 2^77112000 is an apocalyptic number.

77112000 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 77112000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (172602144).

77112000 is an abundant number, since it is smaller than the sum of its proper divisors (268092288).

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

77112000 is a wasteful number, since it uses less digits than its factorization.

77112000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 63 (or 34 counting only the distinct ones).

The product of its (nonzero) digits is 98, while the sum is 18.

The square root of 77112000 is about 8781.3438607083. The cubic root of 77112000 is about 425.6382566850.

Adding to 77112000 its reverse (21177), we get a palindrome (77133177).

The spelling of 77112000 in words is "seventy-seven million, one hundred twelve thousand".