82172404800 has 672 divisors, whose sum is σ = 313284412800. Its totient is φ = 20925112320.

The previous prime is 82172404793. The next prime is 82172404861. The reversal of 82172404800 is 840427128.

82172404800 is a `hidden beast` number, since 8 + 2 + 172 + 4 + 0 + 480 + 0 = 666.

It is a super-2 number, since 2×82172404800² (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 an unprimeable number.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 134049294 + ... + 134049906.

Almost surely, 2^82172404800 is an apocalyptic number.

82172404800 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 82172404800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (156642206400).

82172404800 is an abundant number, since it is smaller than the sum of its proper divisors (231112008000).

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

82172404800 is a wasteful number, since it uses less digits than its factorization.

82172404800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 780 (or 759 counting only the distinct ones).

The product of its (nonzero) digits is 28672, while the sum is 36.

The spelling of 82172404800 in words is "eighty-two billion, one hundred seventy-two million, four hundred four thousand, eight hundred".