82006400 has 144 divisors (see below), whose sum is σ = 236106540. Its totient is φ = 28062720.

The previous prime is 82006391. The next prime is 82006411. The reversal of 82006400 is 460028.

It is a Harshad number since it is a multiple of its sum of digits (20).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 156539 + ... + 157061.

Almost surely, 2^82006400 is an apocalyptic number.

82006400 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 82006400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (118053270).

82006400 is an abundant number, since it is smaller than the sum of its proper divisors (154100140).

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

82006400 is a wasteful number, since it uses less digits than its factorization.

82006400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 561 (or 537 counting only the distinct ones).

The product of its (nonzero) digits is 384, while the sum is 20.

The square root of 82006400 is about 9055.7385121259. The cubic root of 82006400 is about 434.4594509989.

Adding to 82006400 its reverse (460028), we get a palindrome (82466428).

The spelling of 82006400 in words is "eighty-two million, six thousand, four hundred".