75768000 has 448 divisors, whose sum is σ = 319527936. Its totient is φ = 15360000.

The previous prime is 75767983. The next prime is 75768001. The reversal of 75768000 is 86757.

It is a tau number, because it is divible by the number of its divisors (448).

It is a Harshad number since it is a multiple of its sum of digits (33).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (75768001) by changing a digit.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 1847980 + ... + 1848020.

It is an arithmetic number, because the mean of its divisors is an integer number (713232).

Almost surely, 2^75768000 is an apocalyptic number.

75768000 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 75768000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (159763968).

75768000 is an abundant number, since it is smaller than the sum of its proper divisors (243759936).

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

75768000 is a wasteful number, since it uses less digits than its factorization.

75768000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 89 (or 69 counting only the distinct ones).

The product of its (nonzero) digits is 11760, while the sum is 33.

The square root of 75768000 is about 8704.4816043231. The cubic root of 75768000 is about 423.1509054770.

It can be divided in two parts, 7576 and 8000, that added together give a triangular number (15576 = T₁₇₆).

The spelling of 75768000 in words is "seventy-five million, seven hundred sixty-eight thousand".