135416400 has 300 divisors, whose sum is σ = 516818112. Its totient is φ = 30293760.

The previous prime is 135416389. The next prime is 135416419. The reversal of 135416400 is 4614531.

It is a tau number, because it is divible by the number of its divisors (300).

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 59 ways as a sum of consecutive naturals, for example, 2881177 + ... + 2881223.

Almost surely, 2^135416400 is an apocalyptic number.

135416400 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 135416400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (258409056).

135416400 is an abundant number, since it is smaller than the sum of its proper divisors (381401712).

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

135416400 is an equidigital number, since it uses as much as digits as its factorization.

135416400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 96 (or 64 counting only the distinct ones).

The product of its (nonzero) digits is 1440, while the sum is 24.

The square root of 135416400 is about 11636.8552452972. The cubic root of 135416400 is about 513.5196752324.

The spelling of 135416400 in words is "one hundred thirty-five million, four hundred sixteen thousand, four hundred".