40320649728000 has 1248 divisors, whose sum is σ = 153227725129440. Its totient is φ = 10183743897600.

The previous prime is 40320649727993. The next prime is 40320649728013. The reversal of 40320649728000 is 82794602304.

40320649728000 is a `hidden beast` number, since 4 + 0 + 320 + 6 + 49 + 7 + 280 + 0 + 0 = 666.

It can be written as a sum of positive squares in 16 ways, for example, as 31541612580864 + 8779037147136 = 5616192^2 + 2962944^2 .

It is a Harshad number since it is a multiple of its sum of digits (45).

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 95 ways as a sum of consecutive naturals, for example, 7082493154 + ... + 7082498846.

It is an arithmetic number, because the mean of its divisors is an integer number (122778625905).

Almost surely, 2^{40320649728000} is an apocalyptic number.

40320649728000 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 40320649728000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (76613862564720).

40320649728000 is an abundant number, since it is smaller than the sum of its proper divisors (112907075401440).

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

40320649728000 is a wasteful number, since it uses less digits than its factorization.

40320649728000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 5820 (or 5785 counting only the distinct ones).

The product of its (nonzero) digits is 580608, while the sum is 45.

The spelling of 40320649728000 in words is "forty trillion, three hundred twenty billion, six hundred forty-nine million, seven hundred twenty-eight thousand".