82742400 has 432 divisors, whose sum is σ = 338507910. Its totient is φ = 19169280.

The previous prime is 82742357. The next prime is 82742411. The reversal of 82742400 is 424728.

It can be written as a sum of positive squares in 9 ways, for example, as 5184 + 82737216 = 72^2 + 9096^2 .

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 53 ways as a sum of consecutive naturals, for example, 4867192 + ... + 4867208.

Almost surely, 2^82742400 is an apocalyptic number.

82742400 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 82742400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (169253955).

82742400 is an abundant number, since it is smaller than the sum of its proper divisors (255765510).

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

82742400 is a wasteful number, since it uses less digits than its factorization.

82742400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 73 (or 40 counting only the distinct ones).

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

The square root of 82742400 is about 9096.2849559587. The cubic root of 82742400 is about 435.7553266265.

The spelling of 82742400 in words is "eighty-two million, seven hundred forty-two thousand, four hundred".