75840 has 56 divisors (see below), whose sum is σ = 243840. Its totient is φ = 19968.

The previous prime is 75833. The next prime is 75853. The reversal of 75840 is 4857.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a self number, because there is not a number n which added to its sum of digits gives 75840.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 921 + ... + 999.

2⁷⁵⁸⁴⁰ 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 75840, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (121920).

75840 is an abundant number, since it is smaller than the sum of its proper divisors (168000).

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

75840 is a wasteful number, since it uses less digits than its factorization.

75840 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 99 (or 89 counting only the distinct ones).

The product of its (nonzero) digits is 1120, while the sum is 24.

The square root of 75840 is about 275.3906316489. The cubic root of 75840 is about 42.3284898806.

75840 divided by its sum of digits (24) gives a triangular number (3160 = T₇₉).

The spelling of 75840 in words is "seventy-five thousand, eight hundred forty".