417872 has 60 divisors (see below), whose sum is σ = 1038996. Its totient is φ = 161280.

The previous prime is 417869. The next prime is 417881. The reversal of 417872 is 278714.

It can be written as a sum of positive squares in 2 ways, for example, as 38416 + 379456 = 196^2 + 616^2 .

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 10172 + ... + 10212.

2⁴¹⁷⁸⁷² 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 417872, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (519498).

417872 is an abundant number, since it is smaller than the sum of its proper divisors (621124).

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

417872 is a wasteful number, since it uses less digits than its factorization.

417872 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 76 (or 63 counting only the distinct ones).

The product of its digits is 3136, while the sum is 29.

The square root of 417872 is about 646.4301973145. The cubic root of 417872 is about 74.7620309267.

Subtracting from 417872 its product of digits (3136), we obtain a square (414736 = 644²).

The spelling of 417872 in words is "four hundred seventeen thousand, eight hundred seventy-two".