420516000 has 144 divisors (see below), whose sum is σ = 1492539048. Its totient is φ = 112128000.

The previous prime is 420515987. The next prime is 420516001. The reversal of 420516000 is 615024.

It is a happy number.

It can be written as a sum of positive squares in 4 ways, for example, as 124813584 + 295702416 = 11172^2 + 17196^2 .

It is a tau number, because it is divible by the number of its divisors (144).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is not an unprimeable number, because it can be changed into a prime (420516001) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 30160 + ... + 41840.

Almost surely, 2^420516000 is an apocalyptic number.

420516000 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 420516000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (746269524).

420516000 is an abundant number, since it is smaller than the sum of its proper divisors (1072023048).

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

420516000 is a wasteful number, since it uses less digits than its factorization.

420516000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 11712 (or 11691 counting only the distinct ones).

The product of its (nonzero) digits is 240, while the sum is 18.

The square root of 420516000 is about 20506.4867785781. The cubic root of 420516000 is about 749.1938003667.

The spelling of 420516000 in words is "four hundred twenty million, five hundred sixteen thousand".