135585213120 has 672 divisors, whose sum is σ = 555694583808. Its totient is φ = 30824312832.

The previous prime is 135585213067. The next prime is 135585213121. The reversal of 135585213120 is 21312585531.

135585213120 is a `hidden beast` number, since 1 + 3 + 5 + 5 + 8 + 521 + 3 + 120 = 666.

It is a tau number, because it is divible by the number of its divisors (672).

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 (135585213121) by changing a digit.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 121382802 + ... + 121383918.

It is an arithmetic number, because the mean of its divisors is an integer number (826926464).

Almost surely, 2^135585213120 is an apocalyptic number.

135585213120 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 135585213120, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (277847291904).

135585213120 is an abundant number, since it is smaller than the sum of its proper divisors (420109370688).

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

135585213120 is a wasteful number, since it uses less digits than its factorization.

135585213120 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1379 (or 1357 counting only the distinct ones).

The product of its (nonzero) digits is 36000, while the sum is 36.

Adding to 135585213120 its reverse (21312585531), we get a palindrome (156897798651).

The spelling of 135585213120 in words is "one hundred thirty-five billion, five hundred eighty-five million, two hundred thirteen thousand, one hundred twenty".