415272 has 64 divisors (see below), whose sum is σ = 1229760. Its totient is φ = 116160.

The previous prime is 415271. The next prime is 415273. The reversal of 415272 is 272514.

415272 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It is an interprime number because it is at equal distance from previous prime (415271) and next prime (415273).

It is an Ulam number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 415272.

It is not an unprimeable number, because it can be changed into a prime (415271) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 31938 + ... + 31950.

It is an arithmetic number, because the mean of its divisors is an integer number (19215).

2⁴¹⁵²⁷² 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 415272, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (614880).

415272 is an abundant number, since it is smaller than the sum of its proper divisors (814488).

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

415272 is a wasteful number, since it uses less digits than its factorization.

415272 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 55 (or 29 counting only the distinct ones).

The product of its digits is 560, while the sum is 21.

The square root of 415272 is about 644.4160146986. The cubic root of 415272 is about 74.6066517463.

Adding to 415272 its reverse (272514), we get a palindrome (687786).

It can be divided in two parts, 4152 and 72, that added together give a palindrome (4224).

The spelling of 415272 in words is "four hundred fifteen thousand, two hundred seventy-two".