20138414400 has 420 divisors, whose sum is σ = 79724549212. Its totient is φ = 4956733440.

The previous prime is 20138414371. The next prime is 20138414411. The reversal of 20138414400 is 441483102.

20138414400 is a `hidden beast` number, since 201 + 3 + 8 + 414 + 40 + 0 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 203233536 + 19935180864 = 14256^2 + 141192^2 .

It is a super-3 number, since 3×20138414400³ (a number of 32 digits) contains 333 as substring. Note that it is a super-d number also for d = 2.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 59 ways as a sum of consecutive naturals, for example, 1678824 + ... + 1690776.

Almost surely, 2^20138414400 is an apocalyptic number.

20138414400 is a gapful number since it is divisible by the number (20) 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 20138414400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (39862274606).

20138414400 is an abundant number, since it is smaller than the sum of its proper divisors (59586134812).

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

20138414400 is a wasteful number, since it uses less digits than its factorization.

20138414400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 12000 (or 11976 counting only the distinct ones).

The product of its (nonzero) digits is 3072, while the sum is 27.

Adding to 20138414400 its reverse (441483102), we get a palindrome (20579897502).

The spelling of 20138414400 in words is "twenty billion, one hundred thirty-eight million, four hundred fourteen thousand, four hundred".