420814880400 has 480 divisors, whose sum is σ = 1460781504000. Its totient is φ = 103222702080.

The previous prime is 420814880399. The next prime is 420814880401. The reversal of 420814880400 is 4088418024.

It is an interprime number because it is at equal distance from previous prime (420814880399) and next prime (420814880401).

It is not an unprimeable number, because it can be changed into a prime (420814880401) by changing a digit.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 111649716 + ... + 111653484.

It is an arithmetic number, because the mean of its divisors is an integer number (3043294800).

Almost surely, 2^420814880400 is an apocalyptic number.

420814880400 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 420814880400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (730390752000).

420814880400 is an abundant number, since it is smaller than the sum of its proper divisors (1039966623600).

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

420814880400 is a wasteful number, since it uses less digits than its factorization.

420814880400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 3951 (or 3940 counting only the distinct ones).

The product of its (nonzero) digits is 65536, while the sum is 39.

It can be divided in two parts, 42081 and 4880400, that multiplied together give a square (205372112400 = 453180²).

The spelling of 420814880400 in words is "four hundred twenty billion, eight hundred fourteen million, eight hundred eighty thousand, four hundred".