82406400 has 264 divisors, whose sum is σ = 289363920. Its totient is φ = 20643840.

The previous prime is 82406399. The next prime is 82406411. The reversal of 82406400 is 460428.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 2227182 + ... + 2227218.

Almost surely, 2^82406400 is an apocalyptic number.

82406400 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 82406400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (144681960).

82406400 is an abundant number, since it is smaller than the sum of its proper divisors (206957520).

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

82406400 is a wasteful number, since it uses less digits than its factorization.

82406400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 99 (or 76 counting only the distinct ones).

The product of its (nonzero) digits is 1536, while the sum is 24.

The square root of 82406400 is about 9077.7970896027. The cubic root of 82406400 is about 435.1646885998.

Adding to 82406400 its reverse (460428), we get a palindrome (82866828).

The spelling of 82406400 in words is "eighty-two million, four hundred six thousand, four hundred".