417009072 has 80 divisors (see below), whose sum is σ = 1103040512. Its totient is φ = 135717120.

The previous prime is 417009059. The next prime is 417009079. The reversal of 417009072 is 270900714.

It is a super-2 number, since 2×417009072² = 347793132260602368, which contains 22 as substring.

It is not an unprimeable number, because it can be changed into a prime (417009079) 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, 407922 + ... + 408942.

Almost surely, 2^417009072 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 417009072, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (551520256).

417009072 is an abundant number, since it is smaller than the sum of its proper divisors (686031440).

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

417009072 is a wasteful number, since it uses less digits than its factorization.

417009072 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1226 (or 1220 counting only the distinct ones).

The product of its (nonzero) digits is 3528, while the sum is 30.

The square root of 417009072 is about 20420.7999843297. The cubic root of 417009072 is about 747.1053293266.

Adding to 417009072 its reverse (270900714), we get a palindrome (687909786).

The spelling of 417009072 in words is "four hundred seventeen million, nine thousand, seventy-two".