76752000 has 384 divisors, whose sum is σ = 304078320. Its totient is φ = 18432000.

The previous prime is 76751999. The next prime is 76752007. The reversal of 76752000 is 25767.

It can be written as a sum of positive squares in 8 ways, for example, as 6594624 + 70157376 = 2568^2 + 8376^2 .

It is a tau number, because it is divible by the number of its divisors (384).

It is not an unprimeable number, because it can be changed into a prime (76752007) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 1871980 + ... + 1872020.

Almost surely, 2^76752000 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 76752000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (152039160).

76752000 is an abundant number, since it is smaller than the sum of its proper divisors (227326320).

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

76752000 is a wasteful number, since it uses less digits than its factorization.

76752000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 89 (or 64 counting only the distinct ones).

The product of its (nonzero) digits is 2940, while the sum is 27.

The square root of 76752000 is about 8760.8218792531. The cubic root of 76752000 is about 424.9748543369.

Adding to 76752000 its reverse (25767), we get a palindrome (76777767).

The spelling of 76752000 in words is "seventy-six million, seven hundred fifty-two thousand".