407516400 has 240 divisors, whose sum is σ = 1469176800. Its totient is φ = 107274240.

The previous prime is 407516399. The next prime is 407516407. The reversal of 407516400 is 4615704.

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 (27).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (407516407) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 1047406 + ... + 1047794.

It is an arithmetic number, because the mean of its divisors is an integer number (6121570).

Almost surely, 2^407516400 is an apocalyptic number.

407516400 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 407516400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (734588400).

407516400 is an abundant number, since it is smaller than the sum of its proper divisors (1061660400).

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

407516400 is a wasteful number, since it uses less digits than its factorization.

407516400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 513 (or 496 counting only the distinct ones).

The product of its (nonzero) digits is 3360, while the sum is 27.

The square root of 407516400 is about 20187.0354435712. The cubic root of 407516400 is about 741.3927993319.

The spelling of 407516400 in words is "four hundred seven million, five hundred sixteen thousand, four hundred".