434112416400 has 480 divisors, whose sum is σ = 1528357178880. Its totient is φ = 104684912640.

The previous prime is 434112416389. The next prime is 434112416429. The reversal of 434112416400 is 4614211434.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is an unprimeable number.

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 95 ways as a sum of consecutive naturals, for example, 156887817 + ... + 156890583.

It is an arithmetic number, because the mean of its divisors is an integer number (3184077456).

Almost surely, 2^434112416400 is an apocalyptic number.

434112416400 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 434112416400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (764178589440).

434112416400 is an abundant number, since it is smaller than the sum of its proper divisors (1094244762480).

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

434112416400 is a wasteful number, since it uses less digits than its factorization.

434112416400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 3003 (or 2992 counting only the distinct ones).

The product of its (nonzero) digits is 9216, while the sum is 30.

Adding to 434112416400 its reverse (4614211434), we get a palindrome (438726627834).

The spelling of 434112416400 in words is "four hundred thirty-four billion, one hundred twelve million, four hundred sixteen thousand, four hundred".