416352542400 has 504 divisors, whose sum is σ = 1500110196624. Its totient is φ = 109513728000.

The previous prime is 416352542399. The next prime is 416352542401. The reversal of 416352542400 is 4245253614.

416352542400 is a `hidden beast` number, since 4 + 1 + 63 + 52 + 542 + 4 + 0 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (416352542399) and next prime (416352542401).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is not an unprimeable number, because it can be changed into a prime (416352542401) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 679204494 + ... + 679205106.

Almost surely, 2^416352542400 is an apocalyptic number.

416352542400 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 416352542400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (750055098312).

416352542400 is an abundant number, since it is smaller than the sum of its proper divisors (1083757654224).

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

416352542400 is a wasteful number, since it uses less digits than its factorization.

416352542400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1209 (or 1191 counting only the distinct ones).

The product of its (nonzero) digits is 115200, while the sum is 36.

The spelling of 416352542400 in words is "four hundred sixteen billion, three hundred fifty-two million, five hundred forty-two thousand, four hundred".