417112336872 has 768 divisors, whose sum is σ = 1606571366400. Its totient is φ = 94337187840.

The previous prime is 417112336819. The next prime is 417112336877. The reversal of 417112336872 is 278633211714.

417112336872 is a `hidden beast` number, since 417 + 1 + 123 + 36 + 87 + 2 = 666.

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

It is not an unprimeable number, because it can be changed into a prime (417112336877) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 76997908 + ... + 77003324.

It is an arithmetic number, because the mean of its divisors is an integer number (2091889800).

Almost surely, 2^417112336872 is an apocalyptic number.

417112336872 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 417112336872, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (803285683200).

417112336872 is an abundant number, since it is smaller than the sum of its proper divisors (1189459029528).

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

417112336872 is a wasteful number, since it uses less digits than its factorization.

417112336872 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 5526 (or 5519 counting only the distinct ones).

The product of its digits is 338688, while the sum is 45.

The spelling of 417112336872 in words is "four hundred seventeen billion, one hundred twelve million, three hundred thirty-six thousand, eight hundred seventy-two".