417799872 has 252 divisors, whose sum is σ = 1416122136. Its totient is φ = 117411840.

The previous prime is 417799861. The next prime is 417799883. The reversal of 417799872 is 278997714.

417799872 is a `hidden beast` number, since 417 + 79 + 98 + 72 = 666.

It is an interprime number because it is at equal distance from previous prime (417799861) and next prime (417799883).

It is a tau number, because it is divible by the number of its divisors (252).

It is a nude number because it is divisible by every one of its digits.

It is an unprimeable number.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 3189247 + ... + 3189377.

Almost surely, 2^417799872 is an apocalyptic number.

417799872 is a gapful number since it is divisible by the number (42) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 417799872, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (708061068).

417799872 is an abundant number, since it is smaller than the sum of its proper divisors (998322264).

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

417799872 is a wasteful number, since it uses less digits than its factorization.

417799872 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 276 (or 256 counting only the distinct ones).

The product of its digits is 1778112, while the sum is 54.

The square root of 417799872 is about 20440.1534240817. The cubic root of 417799872 is about 747.5772917397.

The spelling of 417799872 in words is "four hundred seventeen million, seven hundred ninety-nine thousand, eight hundred seventy-two".