420107977800 has 1152 divisors, whose sum is σ = 1764172800000. Its totient is φ = 89281543680.

The previous prime is 420107977777. The next prime is 420107977871. The reversal of 420107977800 is 8779701024.

It is a happy number.

420107977800 is a `hidden beast` number, since 420 + 10 + 79 + 77 + 80 + 0 = 666.

It is a super-2 number, since 2×420107977800² (a number of 24 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 287 ways as a sum of consecutive naturals, for example, 692105097 + ... + 692105703.

It is an arithmetic number, because the mean of its divisors is an integer number (1531400000).

Almost surely, 2^420107977800 is an apocalyptic number.

420107977800 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 420107977800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (882086400000).

420107977800 is an abundant number, since it is smaller than the sum of its proper divisors (1344064822200).

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

420107977800 is a wasteful number, since it uses less digits than its factorization.

420107977800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 728 (or 702 counting only the distinct ones).

The product of its (nonzero) digits is 197568, while the sum is 45.

The spelling of 420107977800 in words is "four hundred twenty billion, one hundred seven million, nine hundred seventy-seven thousand, eight hundred".