75684 has 48 divisors (see below), whose sum is σ = 217728. Its totient is φ = 19968.

The previous prime is 75683. The next prime is 75689. The reversal of 75684 is 48657.

75684 = T₄₉ + T₅₀ + ... + T₈₂.

It is a happy number.

It is a Smith number, since the sum of its digits (30) coincides with the sum of the digits of its prime factors.

Its product of digits (6720) is a multiple of the sum of its prime factors (84).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (75683) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 1402 + ... + 1454.

It is an arithmetic number, because the mean of its divisors is an integer number (4536).

2⁷⁵⁶⁸⁴ 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 75684, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (108864).

75684 is an abundant number, since it is smaller than the sum of its proper divisors (142044).

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

75684 is a wasteful number, since it uses less digits than its factorization.

75684 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 84 (or 82 counting only the distinct ones).

The product of its digits is 6720, while the sum is 30.

The square root of 75684 is about 275.1072518128. The cubic root of 75684 is about 42.2994472596.

It can be divided in two parts, 756 and 84, that multiplied together give a square (63504 = 252²).

The spelling of 75684 in words is "seventy-five thousand, six hundred eighty-four".