27638644683672 has 384 divisors, whose sum is σ = 85487403456000. Its totient is φ = 7992150405120.

The previous prime is 27638644683569. The next prime is 27638644683751.

27638644683672 is a `hidden beast` number, since 2 + 7 + 6 + 3 + 8 + 64 + 468 + 36 + 72 = 666.

27638644683672 is nontrivially palindromic in base 10.

It is a super-3 number, since 3×27638644683672³ (a number of 41 digits) contains 333 as substring.

It is a Harshad number since it is a multiple of its sum of digits (72).

It is a self number, because there is not a number n which added to its sum of digits gives 27638644683672.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 748610829 + ... + 748647747.

It is an arithmetic number, because the mean of its divisors is an integer number (222623446500).

Almost surely, 2^{27638644683672} is an apocalyptic number.

27638644683672 is a gapful number since it is divisible by the number (22) 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 27638644683672, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (42743701728000).

27638644683672 is an abundant number, since it is smaller than the sum of its proper divisors (57848758772328).

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

27638644683672 is a wasteful number, since it uses less digits than its factorization.

27638644683672 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 37471 (or 37464 counting only the distinct ones).

The product of its digits is 2341011456, while the sum is 72.

The spelling of 27638644683672 in words is "twenty-seven trillion, six hundred thirty-eight billion, six hundred forty-four million, six hundred eighty-three thousand, six hundred seventy-two".