82124651404800 has 1440 divisors, whose sum is σ = 317873251238400. Its totient is φ = 20186021560320.

The previous prime is 82124651404793. The next prime is 82124651404813. The reversal of 82124651404800 is 840415642128.

82124651404800 is a `hidden beast` number, since 8 + 2 + 1 + 2 + 465 + 140 + 48 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1440).

It is a super-2 number, since 2×82124651404800² (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 143 ways as a sum of consecutive naturals, for example, 70614489019 + ... + 70614490181.

It is an arithmetic number, because the mean of its divisors is an integer number (220745313360).

Almost surely, 2^{82124651404800} is an apocalyptic number.

82124651404800 is a gapful number since it is divisible by the number (80) 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 82124651404800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (158936625619200).

82124651404800 is an abundant number, since it is smaller than the sum of its proper divisors (235748599833600).

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

82124651404800 is a wasteful number, since it uses less digits than its factorization.

82124651404800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2168 (or 2144 counting only the distinct ones).

The product of its (nonzero) digits is 491520, while the sum is 45.

The spelling of 82124651404800 in words is "eighty-two trillion, one hundred twenty-four billion, six hundred fifty-one million, four hundred four thousand, eight hundred".