75960 has 48 divisors (see below), whose sum is σ = 248040. Its totient is φ = 20160.

The previous prime is 75941. The next prime is 75967. The reversal of 75960 is 6957.

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 75960.

It is not an unprimeable number, because it can be changed into a prime (75967) by changing a digit.

75960 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 255 + ... + 465.

2⁷⁵⁹⁶⁰ 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 75960, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (124020).

75960 is an abundant number, since it is smaller than the sum of its proper divisors (172080).

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

75960 is a wasteful number, since it uses less digits than its factorization.

75960 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 228 (or 221 counting only the distinct ones).

The product of its (nonzero) digits is 1890, while the sum is 27.

The square root of 75960 is about 275.6084178685. The cubic root of 75960 is about 42.3508032690.

It can be divided in two parts, 75 and 960, that added together give a triangular number (1035 = T₄₅).

The spelling of 75960 in words is "seventy-five thousand, nine hundred sixty".