106072084800 has 756 divisors, whose sum is σ = 438892838748. Its totient is φ = 24195072000.

The previous prime is 106072084799. The next prime is 106072084819. The reversal of 106072084800 is 8480270601.

106072084800 is a `hidden beast` number, since 1 + 0 + 607 + 2 + 0 + 8 + 48 + 0 + 0 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 5542504704 + 100529580096 = 74448^2 + 317064^2 .

It is a super-2 number, since 2×106072084800² (a number of 23 digits) contains 22 as substring.

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 107 ways as a sum of consecutive naturals, for example, 29619010 + ... + 29622590.

It is an arithmetic number, because the mean of its divisors is an integer number (580546083).

Almost surely, 2^106072084800 is an apocalyptic number.

106072084800 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 106072084800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (219446419374).

106072084800 is an abundant number, since it is smaller than the sum of its proper divisors (332820753948).

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

106072084800 is a wasteful number, since it uses less digits than its factorization.

106072084800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 3648 (or 3619 counting only the distinct ones).

The product of its (nonzero) digits is 21504, while the sum is 36.

The spelling of 106072084800 in words is "one hundred six billion, seventy-two million, eighty-four thousand, eight hundred".