420084000 has 288 divisors, whose sum is σ = 1704882816. Its totient is φ = 95961600.

The previous prime is 420083987. The next prime is 420084013. The reversal of 420084000 is 480024.

It is a happy number.

It is an interprime number because it is at equal distance from previous prime (420083987) and next prime (420084013).

It is a tau number, because it is divible by the number of its divisors (288).

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

It is a super Niven number, because it is divisible the sum of any subset of its (nonzero) digits.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 251167 + ... + 252833.

It is an arithmetic number, because the mean of its divisors is an integer number (5919732).

Almost surely, 2^420084000 is an apocalyptic number.

420084000 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 420084000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (852441408).

420084000 is an abundant number, since it is smaller than the sum of its proper divisors (1284798816).

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

420084000 is a wasteful number, since it uses less digits than its factorization.

420084000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1705 (or 1684 counting only the distinct ones).

The product of its (nonzero) digits is 256, while the sum is 18.

The square root of 420084000 is about 20495.9508196131. The cubic root of 420084000 is about 748.9371612097.

The spelling of 420084000 in words is "four hundred twenty million, eighty-four thousand".