416480400 has 360 divisors, whose sum is σ = 1726571040. Its totient is φ = 95074560.

The previous prime is 416480377. The next prime is 416480417. The reversal of 416480400 is 4084614.

It is a tau number, because it is divible by the number of its divisors (360).

It is a Harshad number since it is a multiple of its sum of digits (27).

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, 528807 + ... + 529593.

Almost surely, 2^416480400 is an apocalyptic number.

416480400 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 416480400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (863285520).

416480400 is an abundant number, since it is smaller than the sum of its proper divisors (1310090640).

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

416480400 is a wasteful number, since it uses less digits than its factorization.

416480400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 828 (or 804 counting only the distinct ones).

The product of its (nonzero) digits is 3072, while the sum is 27.

The square root of 416480400 is about 20407.8514302707. The cubic root of 416480400 is about 746.7894763273.

The spelling of 416480400 in words is "four hundred sixteen million, four hundred eighty thousand, four hundred".