419968 has 32 divisors (see below), whose sum is σ = 890460. Its totient is φ = 196608.

The previous prime is 419959. The next prime is 419999. The reversal of 419968 is 869914.

It can be written as a sum of positive squares in 2 ways, for example, as 419904 + 64 = 648^2 + 8^2 .

It is a tau number, because it is divible by the number of its divisors (32).

It is an unprimeable number.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 2080 + ... + 2272.

2⁴¹⁹⁹⁶⁸ 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 419968, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (445230).

419968 is an abundant number, since it is smaller than the sum of its proper divisors (470492).

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

419968 is a wasteful number, since it uses less digits than its factorization.

419968 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 224 (or 212 counting only the distinct ones).

The product of its digits is 15552, while the sum is 37.

The square root of 419968 is about 648.0493808345. The cubic root of 419968 is about 74.8868218880.

The spelling of 419968 in words is "four hundred nineteen thousand, nine hundred sixty-eight".