45072 has 30 divisors (see below), whose sum is σ = 126542. Its totient is φ = 14976.

The previous prime is 45061. The next prime is 45077. The reversal of 45072 is 27054.

It is a happy number.

45072 is nontrivially palindromic in base 5.

It can be written as a sum of positive squares in only one way, i.e., 24336 + 20736 = 156^2 + 144^2 .

It is a Harshad number since it is a multiple of its sum of digits (18).

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

It is a nialpdrome in base 6 and base 12.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (45077) by changing a digit.

45072 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 5 ways as a sum of consecutive naturals, for example, 13 + ... + 300.

2⁴⁵⁰⁷² 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 45072, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (63271).

45072 is an abundant number, since it is smaller than the sum of its proper divisors (81470).

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

45072 is a wasteful number, since it uses less digits than its factorization.

45072 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 327 (or 318 counting only the distinct ones).

The product of its (nonzero) digits is 280, while the sum is 18.

The square root of 45072 is about 212.3016721554. The cubic root of 45072 is about 35.5878930341.

Subtracting from 45072 its sum of digits (18), we obtain a palindrome (45054).

It can be divided in two parts, 450 and 72, that multiplied together give a square (32400 = 180²).

The spelling of 45072 in words is "forty-five thousand, seventy-two".