416961600 has 336 divisors, whose sum is σ = 1530705600. Its totient is φ = 98508800.

The previous prime is 416961599. The next prime is 416961607. The reversal of 416961600 is 6169614.

416961600 is digitally balanced in base 6, because in such base it contains all the possibile digits an equal number of times.

It is a Harshad number since it is a multiple of its sum of digits (33).

It is not an unprimeable number, because it can be changed into a prime (416961607) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 2798326 + ... + 2798474.

Almost surely, 2^416961600 is an apocalyptic number.

416961600 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 416961600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (765352800).

416961600 is an abundant number, since it is smaller than the sum of its proper divisors (1113744000).

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

416961600 is a wasteful number, since it uses less digits than its factorization.

416961600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 238 (or 223 counting only the distinct ones).

The product of its (nonzero) digits is 7776, while the sum is 33.

The square root of 416961600 is about 20419.6376069704. The cubic root of 416961600 is about 747.0769782806.

The spelling of 416961600 in words is "four hundred sixteen million, nine hundred sixty-one thousand, six hundred".