415872 has 72 divisors (see below), whose sum is σ = 1263015. Its totient is φ = 131328.

The previous prime is 415861. The next prime is 415873. The reversal of 415872 is 278514.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It can be written as a sum of positive squares in only one way, i.e., 207936 + 207936 = 456^2 + 456^2 .

It is a tau number, because it is divible by the number of its divisors (72).

It is an ABA number since it can be written as A⋅B^A, here for A=2, B=456.

It is not an unprimeable number, because it can be changed into a prime (415873) by changing a digit.

415872 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 8 ways as a sum of consecutive naturals, for example, 21879 + ... + 21897.

415872 is a Friedman number, since it can be written as 8*(57*4)^(2*1), using all its digits and the basic arithmetic operations.

2⁴¹⁵⁸⁷² 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 415872

415872 is an abundant number, since it is smaller than the sum of its proper divisors (847143).

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

415872 is a wasteful number, since it uses less digits than its factorization.

415872 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 58 (or 24 counting only the distinct ones).

The product of its digits is 2240, while the sum is 27.

The square root of 415872 is about 644.8813844421. The cubic root of 415872 is about 74.6425659178.

It can be divided in two parts, 4 and 15872, that added together give a square (15876 = 126²).

The spelling of 415872 in words is "four hundred fifteen thousand, eight hundred seventy-two".