417880 has 32 divisors (see below), whose sum is σ = 973440. Its totient is φ = 161280.

The previous prime is 417869. The next prime is 417881. The reversal of 417880 is 88714.

It is a Smith number, since the sum of its digits (28) coincides with the sum of the digits of its prime factors.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (417881) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 1072 + ... + 1408.

It is an arithmetic number, because the mean of its divisors is an integer number (30420).

2⁴¹⁷⁸⁸⁰ is an apocalyptic number.

417880 is a gapful number since it is divisible by the number (40) 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 417880, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (486720).

417880 is an abundant number, since it is smaller than the sum of its proper divisors (555560).

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

417880 is a wasteful number, since it uses less digits than its factorization.

417880 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 379 (or 375 counting only the distinct ones).

The product of its (nonzero) digits is 1792, while the sum is 28.

The square root of 417880 is about 646.4363851146. The cubic root of 417880 is about 74.7625080205.

It can be divided in two parts, 41 and 7880, that added together give a square (7921 = 89²).

The spelling of 417880 in words is "four hundred seventeen thousand, eight hundred eighty".