420688800 has 432 divisors, whose sum is σ = 1798759872. Its totient is φ = 90316800.

The previous prime is 420688787. The next prime is 420688813. The reversal of 420688800 is 8886024.

It is an interprime number because it is at equal distance from previous prime (420688787) and next prime (420688813).

It is a super-3 number, since 3×420688800³ (a number of 27 digits) contains 333 as substring.

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

It is an unprimeable number.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 856555 + ... + 857045.

It is an arithmetic number, because the mean of its divisors is an integer number (4163796).

Almost surely, 2^420688800 is an apocalyptic number.

420688800 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 420688800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (899379936).

420688800 is an abundant number, since it is smaller than the sum of its proper divisors (1378071072).

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

420688800 is a wasteful number, since it uses less digits than its factorization.

420688800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 541 (or 525 counting only the distinct ones).

The product of its (nonzero) digits is 24576, while the sum is 36.

The square root of 420688800 is about 20510.6996467697. The cubic root of 420688800 is about 749.2964068152.

The spelling of 420688800 in words is "four hundred twenty million, six hundred eighty-eight thousand, eight hundred".