75360 has 48 divisors (see below), whose sum is σ = 238896. Its totient is φ = 19968.

The previous prime is 75353. The next prime is 75367. The reversal of 75360 is 6357.

It is an interprime number because it is at equal distance from previous prime (75353) and next prime (75367).

It is a tau number, because it is divible by the number of its divisors (48).

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 75360.

It is not an unprimeable number, because it can be changed into a prime (75367) by changing a digit.

75360 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 402 + ... + 558.

It is an arithmetic number, because the mean of its divisors is an integer number (4977).

2⁷⁵³⁶⁰ 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 75360, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (119448).

75360 is an abundant number, since it is smaller than the sum of its proper divisors (163536).

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

75360 is a wasteful number, since it uses less digits than its factorization.

75360 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 175 (or 167 counting only the distinct ones).

The product of its (nonzero) digits is 630, while the sum is 21.

The square root of 75360 is about 274.5177589884. The cubic root of 75360 is about 42.2390002059.

It can be divided in two parts, 75 and 360, that multiplied together give a cube (27000 = 30³).

The spelling of 75360 in words is "seventy-five thousand, three hundred sixty".