416900400 has 240 divisors, whose sum is σ = 1576470528. Its totient is φ = 92160000.

The previous prime is 416900399. The next prime is 416900443. The reversal of 416900400 is 4009614.

It is a tau number, because it is divible by the number of its divisors (240).

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

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 47 ways as a sum of consecutive naturals, for example, 259600 + ... + 261200.

Almost surely, 2^416900400 is an apocalyptic number.

416900400 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 416900400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (788235264).

416900400 is an abundant number, since it is smaller than the sum of its proper divisors (1159570128).

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

416900400 is a wasteful number, since it uses less digits than its factorization.

416900400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1660 (or 1649 counting only the distinct ones).

The product of its (nonzero) digits is 864, while the sum is 24.

The square root of 416900400 is about 20418.1389945313. The cubic root of 416900400 is about 747.0404254756.

The spelling of 416900400 in words is "four hundred sixteen million, nine hundred thousand, four hundred".