75734400 has 384 divisors, whose sum is σ = 303552000. Its totient is φ = 16558080.

The previous prime is 75734389. The next prime is 75734401. The reversal of 75734400 is 443757.

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

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (75734401) 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, 3292789 + ... + 3292811.

It is an arithmetic number, because the mean of its divisors is an integer number (790500).

Almost surely, 2^75734400 is an apocalyptic number.

75734400 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 75734400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (151776000).

75734400 is an abundant number, since it is smaller than the sum of its proper divisors (227817600).

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

75734400 is a wasteful number, since it uses less digits than its factorization.

75734400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 71 (or 40 counting only the distinct ones).

The product of its (nonzero) digits is 11760, while the sum is 30.

The square root of 75734400 is about 8702.5513500352. The cubic root of 75734400 is about 423.0883462057.

The spelling of 75734400 in words is "seventy-five million, seven hundred thirty-four thousand, four hundred".