75484800 has 144 divisors (see below), whose sum is σ = 269449830. Its totient is φ = 20121600.

The previous prime is 75484793. The next prime is 75484807. The reversal of 75484800 is 848457.

It is an interprime number because it is at equal distance from previous prime (75484793) and next prime (75484807).

It can be written as a sum of positive squares in 3 ways, for example, as 66194496 + 9290304 = 8136^2 + 3048^2 .

It is a tau number, because it is divible by the number of its divisors (144).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is not an unprimeable number, because it can be changed into a prime (75484807) by changing a digit.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 27490 + ... + 30110.

Almost surely, 2^75484800 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 75484800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (134724915).

75484800 is an abundant number, since it is smaller than the sum of its proper divisors (193965030).

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

75484800 is a wasteful number, since it uses less digits than its factorization.

75484800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2651 (or 2631 counting only the distinct ones).

The product of its (nonzero) digits is 35840, while the sum is 36.

The square root of 75484800 is about 8688.1988927510. The cubic root of 75484800 is about 422.6230399210.

The spelling of 75484800 in words is "seventy-five million, four hundred eighty-four thousand, eight hundred".