106314444972000 has 2304 divisors, whose sum is σ = 408736210821120. Its totient is φ = 27123932160000.

The previous prime is 106314444971957. The next prime is 106314444972011. The reversal of 106314444972000 is 279444413601.

106314444972000 is a `hidden beast` number, since 1 + 0 + 6 + 314 + 4 + 44 + 97 + 200 + 0 = 666.

It is a super-2 number, since 2×106314444972000² (a number of 29 digits) contains 22 as substring.

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 383 ways as a sum of consecutive naturals, for example, 614534363914 + ... + 614534364086.

It is an arithmetic number, because the mean of its divisors is an integer number (177402869280).

Almost surely, 2^{106314444972000} is an apocalyptic number.

106314444972000 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 106314444972000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (204368105410560).

106314444972000 is an abundant number, since it is smaller than the sum of its proper divisors (302421765849120).

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

106314444972000 is a wasteful number, since it uses less digits than its factorization.

106314444972000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 496 (or 466 counting only the distinct ones).

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

It can be divided in two parts, 1063144449 and 72000, that added together give a square (1063216449 = 32607²).

The spelling of 106314444972000 in words is "one hundred six trillion, three hundred fourteen billion, four hundred forty-four million, nine hundred seventy-two thousand".