450072 has 96 divisors (see below), whose sum is σ = 1497600. Its totient is φ = 119232.

The previous prime is 450071. The next prime is 450077. The reversal of 450072 is 270054.

It is a happy number.

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (450071) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 9553 + ... + 9599.

It is an arithmetic number, because the mean of its divisors is an integer number (15600).

2⁴⁵⁰⁰⁷² is an apocalyptic number.

450072 is a gapful number since it is divisible by the number (42) 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 450072, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (748800).

450072 is an abundant number, since it is smaller than the sum of its proper divisors (1047528).

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

450072 is a wasteful number, since it uses less digits than its factorization.

450072 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 85 (or 78 counting only the distinct ones).

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

The square root of 450072 is about 670.8740567349. The cubic root of 450072 is about 76.6350300050.

Subtracting from 450072 its sum of digits (18), we obtain a palindrome (450054).

The spelling of 450072 in words is "four hundred fifty thousand, seventy-two".