102713738400 has 1296 divisors, whose sum is σ = 463875310080. Its totient is φ = 20918476800.

The previous prime is 102713738249. The next prime is 102713738437. The reversal of 102713738400 is 4837317201.

102713738400 is a `hidden beast` number, since 1 + 0 + 271 + 3 + 7 + 384 + 0 + 0 = 666.

It is a super-2 number, since 2×102713738400² (a number of 23 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is an unprimeable number.

It is a polite number, since it can be written in 215 ways as a sum of consecutive naturals, for example, 264045406 + ... + 264045794.

It is an arithmetic number, because the mean of its divisors is an integer number (357928480).

Almost surely, 2^102713738400 is an apocalyptic number.

102713738400 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 102713738400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (231937655040).

102713738400 is an abundant number, since it is smaller than the sum of its proper divisors (361161571680).

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

102713738400 is a wasteful number, since it uses less digits than its factorization.

102713738400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 479 (or 450 counting only the distinct ones).

The product of its (nonzero) digits is 28224, while the sum is 36.

The spelling of 102713738400 in words is "one hundred two billion, seven hundred thirteen million, seven hundred thirty-eight thousand, four hundred".