420456960 has 640 divisors, whose sum is σ = 1885593600. Its totient is φ = 86261760.

The previous prime is 420456941. The next prime is 420456961. The reversal of 420456960 is 69654024.

It is a tau number, because it is divible by the number of its divisors (640).

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

It is not an unprimeable number, because it can be changed into a prime (420456961) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 5322201 + ... + 5322279.

It is an arithmetic number, because the mean of its divisors is an integer number (2946240).

Almost surely, 2^420456960 is an apocalyptic number.

420456960 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 420456960, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (942796800).

420456960 is an abundant number, since it is smaller than the sum of its proper divisors (1465136640).

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

420456960 is a wasteful number, since it uses less digits than its factorization.

420456960 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 129 (or 107 counting only the distinct ones).

The product of its (nonzero) digits is 51840, while the sum is 36.

The square root of 420456960 is about 20505.0471835595. The cubic root of 420456960 is about 749.1587367209.

The spelling of 420456960 in words is "four hundred twenty million, four hundred fifty-six thousand, nine hundred sixty".