3612561638400 has 3168 divisors, whose sum is σ = 16391326887936. Its totient is φ = 776355840000.

The previous prime is 3612561638359. The next prime is 3612561638471. The reversal of 3612561638400 is 48361652163.

3612561638400 is a `hidden beast` number, since 3 + 6 + 1 + 2 + 5 + 6 + 1 + 638 + 4 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (3168).

It is a super-3 number, since 3×3612561638400³ (a number of 39 digits) contains 333 as substring.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 287 ways as a sum of consecutive naturals, for example, 27576806335 + ... + 27576806465.

It is an arithmetic number, because the mean of its divisors is an integer number (5174029952).

Almost surely, 2^{3612561638400} is an apocalyptic number.

3612561638400 is a gapful number since it is divisible by the number (30) 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 3612561638400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (8195663443968).

3612561638400 is an abundant number, since it is smaller than the sum of its proper divisors (12778765249536).

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

3612561638400 is a wasteful number, since it uses less digits than its factorization.

3612561638400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 231 (or 196 counting only the distinct ones).

The product of its (nonzero) digits is 622080, while the sum is 45.

The spelling of 3612561638400 in words is "three trillion, six hundred twelve billion, five hundred sixty-one million, six hundred thirty-eight thousand, four hundred".