338253893222400 has 2025 divisors, whose sum is σ = 1307507229027153. Its totient is φ = 86443838668800.

The previous prime is 338253893222381. The next prime is 338253893222417. The reversal of 338253893222400 is 4222398352833.

It is a happy number.

The square root of 338253893222400 is 18391680.

It is a perfect power (a square), and thus also a powerful number.

338253893222400 is a `hidden beast` number, since 3 + 3 + 8 + 2 + 5 + 3 + 8 + 9 + 3 + 222 + 400 = 666.

It can be written as a sum of positive squares in only one way, i.e., 121771401560064 + 216482491662336 = 11035008^2 + 14713344^2 .

It is a tau number, because it is divible by the number of its divisors (2025).

It is a super-2 number, since 2×338253893222400² (a number of 30 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (54).

It is an unprimeable number.

It is a polite number, since it can be written in 134 ways as a sum of consecutive naturals, for example, 3284018380749 + ... + 3284018380851.

Almost surely, 2^{338253893222400} is an apocalyptic number.

338253893222400 is a gapful number since it is divisible by the number (30) formed by its first and last digit.

338253893222400 is the 18391680-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 338253893222400

338253893222400 is an abundant number, since it is smaller than the sum of its proper divisors (969253335804753).

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

338253893222400 is an frugal number, since it uses more digits than its factorization.

338253893222400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 318 (or 144 counting only the distinct ones).

The product of its (nonzero) digits is 14929920, while the sum is 54.

The spelling of 338253893222400 in words is "three hundred thirty-eight trillion, two hundred fifty-three billion, eight hundred ninety-three million, two hundred twenty-two thousand, four hundred".