414820800 has 126 divisors (see below), whose sum is σ = 1474422248. Its totient is φ = 110615040.

The previous prime is 414820781. The next prime is 414820817. The reversal of 414820800 is 8028414.

It is a super-2 number, since 2×414820800² = 344152592225280000, which contains 22 as substring.

It is a congruent number.

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 17 ways as a sum of consecutive naturals, for example, 4 + ... + 28803.

Almost surely, 2^414820800 is an apocalyptic number.

414820800 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 414820800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (737211124).

414820800 is an abundant number, since it is smaller than the sum of its proper divisors (1059601448).

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

414820800 is a wasteful number, since it uses less digits than its factorization.

414820800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 28835 (or 28817 counting only the distinct ones).

The product of its (nonzero) digits is 2048, while the sum is 27.

The square root of 414820800 is about 20367.1500215420. The cubic root of 414820800 is about 745.7962149444.

The spelling of 414820800 in words is "four hundred fourteen million, eight hundred twenty thousand, eight hundred".