3672864000 has 720 divisors, whose sum is σ = 14854279440. Its totient is φ = 895795200.

The previous prime is 3672863983. The next prime is 3672864023. The reversal of 3672864000 is 4682763.

3672864000 is a `hidden beast` number, since 3 + 6 + 7 + 2 + 8 + 640 + 0 + 0 = 666.

3672864000 is digitally balanced in base 2 and base 4, because in such bases it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in 8 ways, for example, as 1522872576 + 2149991424 = 39024^2 + 46368^2 .

It is a tau number, because it is divible by the number of its divisors (720).

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 79 ways as a sum of consecutive naturals, for example, 33695946 + ... + 33696054.

Almost surely, 2^3672864000 is an apocalyptic number.

3672864000 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 3672864000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (7427139720).

3672864000 is an abundant number, since it is smaller than the sum of its proper divisors (11181415440).

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

3672864000 is a wasteful number, since it uses less digits than its factorization.

3672864000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 165 (or 132 counting only the distinct ones).

The product of its (nonzero) digits is 48384, while the sum is 36.

The square root of 3672864000 is about 60604.1582731746. The cubic root of 3672864000 is about 1542.8899463925.

The spelling of 3672864000 in words is "three billion, six hundred seventy-two million, eight hundred sixty-four thousand".