413973072 has 80 divisors (see below), whose sum is σ = 1204625280. Its totient is φ = 136090368.

The previous prime is 413973071. The next prime is 413973139. The reversal of 413973072 is 270379314.

It is a super-2 number, since 2×413973072² = 342747408682234368, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (413973071) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 24973 + ... + 38099.

It is an arithmetic number, because the mean of its divisors is an integer number (15057816).

Almost surely, 2^413973072 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 413973072, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (602312640).

413973072 is an abundant number, since it is smaller than the sum of its proper divisors (790652208).

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

413973072 is a wasteful number, since it uses less digits than its factorization.

413973072 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 13217 (or 13205 counting only the distinct ones).

The product of its (nonzero) digits is 31752, while the sum is 36.

The square root of 413973072 is about 20346.3282191161. The cubic root of 413973072 is about 745.2878319671.

The spelling of 413973072 in words is "four hundred thirteen million, nine hundred seventy-three thousand, seventy-two".