8200742400 has 480 divisors, whose sum is σ = 30672813600. Its totient is φ = 2145484800.

The previous prime is 8200742317. The next prime is 8200742413. The reversal of 8200742400 is 42470028.

It is a tau number, because it is divible by the number of its divisors (480).

It is a super-2 number, since 2×8200742400² (a number of 21 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 21081406 + ... + 21081794.

It is an arithmetic number, because the mean of its divisors is an integer number (63901695).

Almost surely, 2^8200742400 is an apocalyptic number.

8200742400 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 8200742400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (15336406800).

8200742400 is an abundant number, since it is smaller than the sum of its proper divisors (22472071200).

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

8200742400 is a wasteful number, since it uses less digits than its factorization.

8200742400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 487 (or 460 counting only the distinct ones).

The product of its (nonzero) digits is 3584, while the sum is 27.

The square root of 8200742400 is about 90557.9505068440. The cubic root of 8200742400 is about 2016.5905299520.

The spelling of 8200742400 in words is "eight billion, two hundred million, seven hundred forty-two thousand, four hundred".