12742400102400 has 1872 divisors, whose sum is σ = 50309997454080. Its totient is φ = 3069601382400.

The previous prime is 12742400102387. The next prime is 12742400102413. The reversal of 12742400102400 is 420100424721.

12742400102400 is a `hidden beast` number, since 1 + 2 + 7 + 4 + 2 + 400 + 10 + 240 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (12742400102387) and next prime (12742400102413).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 53315481481 + ... + 53315481719.

It is an arithmetic number, because the mean of its divisors is an integer number (26874998640).

Almost surely, 2^{12742400102400} is an apocalyptic number.

12742400102400 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 12742400102400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (25154998727040).

12742400102400 is an abundant number, since it is smaller than the sum of its proper divisors (37567597351680).

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

12742400102400 is a wasteful number, since it uses less digits than its factorization.

12742400102400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 420 (or 390 counting only the distinct ones).

The product of its (nonzero) digits is 3584, while the sum is 27.

The spelling of 12742400102400 in words is "twelve trillion, seven hundred forty-two billion, four hundred million, one hundred two thousand, four hundred".