416720400 has 120 divisors (see below), whose sum is σ = 1341402240. Its totient is φ = 110584320.

The previous prime is 416720399. The next prime is 416720431. The reversal of 416720400 is 4027614.

It is a tau number, because it is divible by the number of its divisors (120).

It is a Harshad number since it is a multiple of its sum of digits (24).

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 286074 + ... + 287526.

It is an arithmetic number, because the mean of its divisors is an integer number (11178352).

Almost surely, 2^416720400 is an apocalyptic number.

416720400 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 416720400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (670701120).

416720400 is an abundant number, since it is smaller than the sum of its proper divisors (924681840).

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

416720400 is a wasteful number, since it uses less digits than its factorization.

416720400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1713 (or 1702 counting only the distinct ones).

The product of its (nonzero) digits is 1344, while the sum is 24.

The square root of 416720400 is about 20413.7306732503. The cubic root of 416720400 is about 746.9328964881.

The spelling of 416720400 in words is "four hundred sixteen million, seven hundred twenty thousand, four hundred".