45642009600 has 1584 divisors, whose sum is σ = 199569726720. Its totient is φ = 10218700800.

The previous prime is 45642009593. The next prime is 45642009667. The reversal of 45642009600 is 690024654.

45642009600 is a `hidden beast` number, since 4 + 5 + 6 + 42 + 0 + 0 + 9 + 600 = 666.

It is a tau number, because it is divible by the number of its divisors (1584).

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

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 1573862386 + ... + 1573862414.

Almost surely, 2^45642009600 is an apocalyptic number.

45642009600 is a gapful number since it is divisible by the number (40) 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 45642009600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (99784863360).

45642009600 is an abundant number, since it is smaller than the sum of its proper divisors (153927717120).

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

45642009600 is a wasteful number, since it uses less digits than its factorization.

45642009600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 108 (or 73 counting only the distinct ones).

The product of its (nonzero) digits is 51840, while the sum is 36.

It can be divided in two parts, 4564200 and 9600, that added together give a triangular number (4573800 = T₃₀₂₄).

The spelling of 45642009600 in words is "forty-five billion, six hundred forty-two million, nine thousand, six hundred".