78400 has 63 divisors (see below), whose sum is σ = 224409. Its totient is φ = 26880.

The previous prime is 78367. The next prime is 78401. The reversal of 78400 is 487.

78400 = T₂₇₉ + T₂₈₀.

It is a happy number.

The square root of 78400 is 280.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in only one way, i.e., 28224 + 50176 = 168^2 + 224^2 .

It is a super-2 number, since 2×78400² = 12293120000, which contains 22 as substring.

It is a Duffinian number.

It is a nialpdrome in base 7.

It is a zygodrome in base 7.

It is not an unprimeable number, because it can be changed into a prime (78401) by changing a digit.

78400 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 8 ways as a sum of consecutive naturals, for example, 11197 + ... + 11203.

2⁷⁸⁴⁰⁰ is an apocalyptic number.

78400 is a gapful number since it is divisible by the number (70) formed by its first and last digit.

78400 is the 280-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 78400

78400 is an abundant number, since it is smaller than the sum of its proper divisors (146009).

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

78400 is a wasteful number, since it uses less digits than its factorization.

78400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 36 (or 14 counting only the distinct ones).

The product of its (nonzero) digits is 224, while the sum is 19.

The cubic root of 78400 is about 42.7994992226.

Adding to 78400 its reverse (487), we get a palindrome (78887).

The spelling of 78400 in words is "seventy-eight thousand, four hundred".