72045464961600 has 567 divisors, whose sum is σ = 277330180838529. Its totient is φ = 17731008921600.

The previous prime is 72045464961583. The next prime is 72045464961607. The reversal of 72045464961600 is 616946454027.

The square root of 72045464961600 is 8487960.

It is a perfect power (a square), and thus also a powerful number.

72045464961600 is a `hidden beast` number, since 7 + 2 + 0 + 4 + 546 + 4 + 96 + 1 + 6 + 0 + 0 = 666.

It can be written as a sum of positive squares in 13 ways, for example, as 56139534287424 + 15905930674176 = 7492632^2 + 3988224^2 .

It is not an unprimeable number, because it can be changed into a prime (72045464961607) by changing a digit.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 13241214880 + ... + 13241220320.

Almost surely, 2^{72045464961600} is an apocalyptic number.

72045464961600 is the 8487960-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 72045464961600

72045464961600 is an abundant number, since it is smaller than the sum of its proper divisors (205284715876929).

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

72045464961600 is an equidigital number, since it uses as much as digits as its factorization.

72045464961600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 10936 (or 5464 counting only the distinct ones).

The product of its (nonzero) digits is 8709120, while the sum is 54.

The spelling of 72045464961600 in words is "seventy-two trillion, forty-five billion, four hundred sixty-four million, nine hundred sixty-one thousand, six hundred".