417106872 has 288 divisors, whose sum is σ = 1438819200. Its totient is φ = 106838784.

The previous prime is 417106861. The next prime is 417106903. The reversal of 417106872 is 278601714.

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 5025343 + ... + 5025425.

It is an arithmetic number, because the mean of its divisors is an integer number (4995900).

Almost surely, 2^417106872 is an apocalyptic number.

417106872 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 417106872, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (719409600).

417106872 is an abundant number, since it is smaller than the sum of its proper divisors (1021712328).

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

417106872 is a wasteful number, since it uses less digits than its factorization.

417106872 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 187 (or 167 counting only the distinct ones).

The product of its (nonzero) digits is 18816, while the sum is 36.

The square root of 417106872 is about 20423.1944612002. The cubic root of 417106872 is about 747.1637302862.

The spelling of 417106872 in words is "four hundred seventeen million, one hundred six thousand, eight hundred seventy-two".