75972 has 24 divisors (see below), whose sum is σ = 191296. Its totient is φ = 23328.

The previous prime is 75967. The next prime is 75979. The reversal of 75972 is 27957.

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.

It is a plaindrome in base 15.

It is not an unprimeable number, because it can be changed into a prime (75979) by changing a digit.

75972 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, 88 + ... + 399.

2⁷⁵⁹⁷² is an apocalyptic number.

It is an amenable number.

75972 is an abundant number, since it is smaller than the sum of its proper divisors (115324).

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

It is a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (95648).

75972 is a wasteful number, since it uses less digits than its factorization.

75972 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 507 (or 505 counting only the distinct ones).

The product of its digits is 4410, while the sum is 30.

The square root of 75972 is about 275.6301870260. The cubic root of 75972 is about 42.3530333150.

It can be divided in two parts, 75 and 972, that multiplied together give a square (72900 = 270²).

The spelling of 75972 in words is "seventy-five thousand, nine hundred seventy-two".