45672 has 32 divisors (see below), whose sum is σ = 125280. Its totient is φ = 13760.

The previous prime is 45667. The next prime is 45673. The reversal of 45672 is 27654.

It is a happy number.

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

It is an Ulam number.

It is an alternating number because its digits alternate between even and odd.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 45672.

It is not an unprimeable number, because it can be changed into a prime (45673) by changing a digit.

45672 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

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 7 ways as a sum of consecutive naturals, for example, 178 + ... + 350.

It is an arithmetic number, because the mean of its divisors is an integer number (3915).

2⁴⁵⁶⁷² 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 45672, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (62640).

45672 is an abundant number, since it is smaller than the sum of its proper divisors (79608).

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

45672 is a wasteful number, since it uses less digits than its factorization.

45672 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 193 (or 189 counting only the distinct ones).

The product of its digits is 1680, while the sum is 24.

The square root of 45672 is about 213.7100839923. The cubic root of 45672 is about 35.7451131925.

It can be divided in two parts, 456 and 72, that added together give a triangular number (528 = T₃₂).

The spelling of 45672 in words is "forty-five thousand, six hundred seventy-two".