133968038400 has 1260 divisors, whose sum is σ = 580870974222. Its totient is φ = 30516756480.

The previous prime is 133968038389. The next prime is 133968038417. The reversal of 133968038400 is 4830869331.

133968038400 is a `hidden beast` number, since 133 + 9 + 6 + 80 + 38 + 400 = 666.

It can be written as a sum of positive squares in 3 ways, for example, as 125180100864 + 8787937536 = 353808^2 + 93744^2 .

It is a tau number, because it is divible by the number of its divisors (1260).

It is a Harshad number since it is a multiple of its sum of digits (45).

It is an unprimeable number.

It is a polite number, since it can be written in 125 ways as a sum of consecutive naturals, for example, 457228654 + ... + 457228946.

Almost surely, 2^133968038400 is an apocalyptic number.

133968038400 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 133968038400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (290435487111).

133968038400 is an abundant number, since it is smaller than the sum of its proper divisors (446902935822).

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

133968038400 is an frugal number, since it uses more digits than its factorization.

133968038400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 353 (or 310 counting only the distinct ones).

The product of its (nonzero) digits is 373248, while the sum is 45.

The spelling of 133968038400 in words is "one hundred thirty-three billion, nine hundred sixty-eight million, thirty-eight thousand, four hundred".