1006365945600 has 1728 divisors, whose sum is σ = 4143214817280. Its totient is φ = 237817036800.

The previous prime is 1006365945539. The next prime is 1006365945601. The reversal of 1006365945600 is 65495636001.

1006365945600 is a `hidden beast` number, since 1 + 0 + 0 + 6 + 3 + 6 + 594 + 56 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1728).

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (1006365945601) by changing a digit.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 3915820672 + ... + 3915820928.

It is an arithmetic number, because the mean of its divisors is an integer number (2397693760).

Almost surely, 2^{1006365945600} is an apocalyptic number.

1006365945600 is a gapful number since it is divisible by the number (10) 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 1006365945600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2071607408640).

1006365945600 is an abundant number, since it is smaller than the sum of its proper divisors (3136848871680).

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

1006365945600 is a wasteful number, since it uses less digits than its factorization.

1006365945600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 383 (or 358 counting only the distinct ones).

The product of its (nonzero) digits is 583200, while the sum is 45.

The spelling of 1006365945600 in words is "one trillion, six billion, three hundred sixty-five million, nine hundred forty-five thousand, six hundred".