77952000 has 352 divisors, whose sum is σ = 306558720. Its totient is φ = 17203200.

The previous prime is 77951999. The next prime is 77952019. The reversal of 77952000 is 25977.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 2687986 + ... + 2688014.

Almost surely, 2^77952000 is an apocalyptic number.

77952000 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 77952000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (153279360).

77952000 is an abundant number, since it is smaller than the sum of its proper divisors (228606720).

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

77952000 is a wasteful number, since it uses less digits than its factorization.

77952000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 74 (or 46 counting only the distinct ones).

The product of its (nonzero) digits is 4410, while the sum is 30.

The square root of 77952000 is about 8829.0429832457. The cubic root of 77952000 is about 427.1782059047.

Adding to 77952000 its reverse (25977), we get a palindrome (77977977).

The spelling of 77952000 in words is "seventy-seven million, nine hundred fifty-two thousand".