135766400 has 384 divisors, whose sum is σ = 455328000. Its totient is φ = 38707200.

The previous prime is 135766399. The next prime is 135766417. The reversal of 135766400 is 4667531.

It is a Harshad number since it is a multiple of its sum of digits (32).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 4681586 + ... + 4681614.

It is an arithmetic number, because the mean of its divisors is an integer number (1185750).

Almost surely, 2^135766400 is an apocalyptic number.

135766400 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 135766400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (227664000).

135766400 is an abundant number, since it is smaller than the sum of its proper divisors (319561600).

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

135766400 is a wasteful number, since it uses less digits than its factorization.

135766400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 90 (or 73 counting only the distinct ones).

The product of its (nonzero) digits is 15120, while the sum is 32.

The square root of 135766400 is about 11651.8839678397. The cubic root of 135766400 is about 513.9617124402.

The spelling of 135766400 in words is "one hundred thirty-five million, seven hundred sixty-six thousand, four hundred".