77472 has 36 divisors (see below), whose sum is σ = 221130. Its totient is φ = 25728.

The previous prime is 77471. The next prime is 77477. The reversal of 77472 is 27477.

It is a happy number.

It can be written as a sum of positive squares in only one way, i.e., 76176 + 1296 = 276^2 + 36^2 .

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

It is not an unprimeable number, because it can be changed into a prime (77471) by changing a digit.

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 5 ways as a sum of consecutive naturals, for example, 154 + ... + 422.

2⁷⁷⁴⁷² is an apocalyptic number.

77472 is a gapful number since it is divisible by the number (72) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 77472, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (110565).

77472 is an abundant number, since it is smaller than the sum of its proper divisors (143658).

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

77472 is a wasteful number, since it uses less digits than its factorization.

77472 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 285 (or 274 counting only the distinct ones).

The product of its digits is 2744, while the sum is 27.

The square root of 77472 is about 278.3379241138. The cubic root of 77472 is about 42.6299597489.

The spelling of 77472 in words is "seventy-seven thousand, four hundred seventy-two", and thus it is an iban number.