420512000 has 144 divisors (see below), whose sum is σ = 1110603312. Its totient is φ = 158105600.

The previous prime is 420511981. The next prime is 420512003. The reversal of 420512000 is 215024.

It can be written as a sum of positive squares in 8 ways, for example, as 184090624 + 236421376 = 13568^2 + 15376^2 .

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (420512003) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 543614 + ... + 544386.

It is an arithmetic number, because the mean of its divisors is an integer number (7712523).

Almost surely, 2^420512000 is an apocalyptic number.

420512000 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 420512000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (555301656).

420512000 is an abundant number, since it is smaller than the sum of its proper divisors (690091312).

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

420512000 is an equidigital number, since it uses as much as digits as its factorization.

420512000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 821 (or 797 counting only the distinct ones).

The product of its (nonzero) digits is 80, while the sum is 14.

The square root of 420512000 is about 20506.3892482319. The cubic root of 420512000 is about 749.1914248846.

Adding to 420512000 its reverse (215024), we get a palindrome (420727024).

The spelling of 420512000 in words is "four hundred twenty million, five hundred twelve thousand".