46638633683664 has 360 divisors, whose sum is σ = 147418202063496. Its totient is φ = 13744152576000.

The previous prime is 46638633683657. The next prime is 46638633683669.

46638633683664 is a `hidden beast` number, since 46 + 63 + 86 + 3 + 368 + 36 + 64 = 666.

46638633683664 is nontrivially palindromic in base 10.

It can be written as a sum of positive squares in 4 ways, for example, as 10330689600 + 46628302994064 = 101640^2 + 6828492^2 .

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

It is a nude number because it is divisible by every one of its digits.

It is a junction number, because it is equal to n+sod(n) for n = 46638633683592 and 46638633683601.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (46638633683669) by changing a digit.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 1387996464 + ... + 1388030064.

Almost surely, 2^{46638633683664} is an apocalyptic number.

46638633683664 is a gapful number since it is divisible by the number (44) 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 46638633683664, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (73709101031748).

46638633683664 is an abundant number, since it is smaller than the sum of its proper divisors (100779568379832).

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

46638633683664 is a wasteful number, since it uses less digits than its factorization.

46638633683664 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 35827 (or 35807 counting only the distinct ones).

The product of its digits is 3869835264, while the sum is 72.

The spelling of 46638633683664 in words is "forty-six trillion, six hundred thirty-eight billion, six hundred thirty-three million, six hundred eighty-three thousand, six hundred sixty-four".