13138178400 has 288 divisors, whose sum is σ = 47648200320. Its totient is φ = 3493808640.

The previous prime is 13138178369. The next prime is 13138178407. The reversal of 13138178400 is 487183131.

It is a tau number, because it is divible by the number of its divisors (288).

It is a super-2 number, since 2×13138178400² (a number of 21 digits) contains 22 as substring.

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (13138178407) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 11296219 + ... + 11297381.

It is an arithmetic number, because the mean of its divisors is an integer number (165445140).

Almost surely, 2^13138178400 is an apocalyptic number.

13138178400 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 13138178400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (23824100160).

13138178400 is an abundant number, since it is smaller than the sum of its proper divisors (34510021920).

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

13138178400 is a wasteful number, since it uses less digits than its factorization.

13138178400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1715 (or 1696 counting only the distinct ones).

The product of its (nonzero) digits is 16128, while the sum is 36.

The spelling of 13138178400 in words is "thirteen billion, one hundred thirty-eight million, one hundred seventy-eight thousand, four hundred".