405072 has 60 divisors (see below), whose sum is σ = 1184820. Its totient is φ = 129024.

The previous prime is 405071. The next prime is 405073. The reversal of 405072 is 270504.

It is a happy number.

It is an interprime number because it is at equal distance from previous prime (405071) and next prime (405073).

It can be written as a sum of positive squares in 2 ways, for example, as 197136 + 207936 = 444^2 + 456^2 .

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 (405071) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 4128 + ... + 4224.

It is an arithmetic number, because the mean of its divisors is an integer number (19747).

2⁴⁰⁵⁰⁷² 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 405072, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (592410).

405072 is an abundant number, since it is smaller than the sum of its proper divisors (779748).

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

405072 is a wasteful number, since it uses less digits than its factorization.

405072 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 140 (or 131 counting only the distinct ones).

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

The square root of 405072 is about 636.4526690965. The cubic root of 405072 is about 73.9907463471.

Adding to 405072 its reverse (270504), we get a palindrome (675576).

It can be divided in two parts, 4050 and 72, that multiplied together give a square (291600 = 540²).

The spelling of 405072 in words is "four hundred five thousand, seventy-two".