420414000 has 160 divisors (see below), whose sum is σ = 1389286080. Its totient is φ = 109312000.

The previous prime is 420413947. The next prime is 420414019. The reversal of 420414000 is 414024.

It is a Harshad number since it is a multiple of its sum of digits (15).

It is an unprimeable number.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 245146 + ... + 246854.

It is an arithmetic number, because the mean of its divisors is an integer number (8683038).

Almost surely, 2^420414000 is an apocalyptic number.

420414000 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 420414000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (694643040).

420414000 is an abundant number, since it is smaller than the sum of its proper divisors (968872080).

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

420414000 is a wasteful number, since it uses less digits than its factorization.

420414000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1776 (or 1760 counting only the distinct ones).

The product of its (nonzero) digits is 128, while the sum is 15.

The square root of 420414000 is about 20503.9996098322. Note that the first 3 decimals coincide. The cubic root of 420414000 is about 749.1332208667.

Adding to 420414000 its reverse (414024), we get a palindrome (420828024).

The spelling of 420414000 in words is "four hundred twenty million, four hundred fourteen thousand".