75744 has 36 divisors (see below), whose sum is σ = 216216. Its totient is φ = 25152.

The previous prime is 75743. The next prime is 75767. The reversal of 75744 is 44757.

75744 = T₆₁ + T₆₂ + ... + T₈₇.

It is a tau number, because it is divible by the number of its divisors (36).

It is a Smith number, since the sum of its digits (27) coincides with the sum of the digits of its prime factors.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (75743) by changing a digit.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 157 + ... + 419.

It is an arithmetic number, because the mean of its divisors is an integer number (6006).

2⁷⁵⁷⁴⁴ 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 75744, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (108108).

75744 is an abundant number, since it is smaller than the sum of its proper divisors (140472).

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

75744 is a wasteful number, since it uses less digits than its factorization.

75744 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 279 (or 268 counting only the distinct ones).

The product of its digits is 3920, while the sum is 27.

The square root of 75744 is about 275.2162785883. The cubic root of 75744 is about 42.3106222171.

Subtracting from 75744 its product of digits (3920), we obtain a square (71824 = 268²).

The spelling of 75744 in words is "seventy-five thousand, seven hundred forty-four".