135314414400 has 336 divisors, whose sum is σ = 486798396480. Its totient is φ = 32634470400.

The previous prime is 135314414393. The next prime is 135314414413. The reversal of 135314414400 is 4414413531.

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

It is a congruent number.

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 47 ways as a sum of consecutive naturals, for example, 10395096 + ... + 10408104.

Almost surely, 2^135314414400 is an apocalyptic number.

135314414400 is a gapful number since it is divisible by the number (10) 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 135314414400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (243399198240).

135314414400 is an abundant number, since it is smaller than the sum of its proper divisors (351483982080).

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

135314414400 is a wasteful number, since it uses less digits than its factorization.

135314414400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 13242 (or 13227 counting only the distinct ones).

The product of its (nonzero) digits is 11520, while the sum is 30.

Adding to 135314414400 its reverse (4414413531), we get a palindrome (139728827931).

The spelling of 135314414400 in words is "one hundred thirty-five billion, three hundred fourteen million, four hundred fourteen thousand, four hundred".