83517945772800 has 3456 divisors, whose sum is σ = 369325993623552. Its totient is φ = 16244111769600.

The previous prime is 83517945772799. The next prime is 83517945772813. The reversal of 83517945772800 is 827754971538.

It is a super-3 number, since 3×83517945772800³ (a number of 43 digits) contains 333 as substring. Note that it is a super-d number also for d = 2.

It is a Harshad number since it is a multiple of its sum of digits (66).

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, 218062521409 + ... + 218062521791.

It is an arithmetic number, because the mean of its divisors is an integer number (106865160192).

Almost surely, 2^{83517945772800} is an apocalyptic number.

83517945772800 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 83517945772800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (184662996811776).

83517945772800 is an abundant number, since it is smaller than the sum of its proper divisors (285808047850752).

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

83517945772800 is a wasteful number, since it uses less digits than its factorization.

83517945772800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 528 (or 487 counting only the distinct ones).

The product of its (nonzero) digits is 118540800, while the sum is 66.

The spelling of 83517945772800 in words is "eighty-three trillion, five hundred seventeen billion, nine hundred forty-five million, seven hundred seventy-two thousand, eight hundred".