48400 has 45 divisors (see below), whose sum is σ = 127813. Its totient is φ = 17600.

The previous prime is 48397. The next prime is 48407. The reversal of 48400 is 484.

48400 = T₂₁₉ + T₂₂₀.

The square root of 48400 is 220.

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., 17424 + 30976 = 132^2 + 176^2 .

It is a Harshad number since it is a multiple of its sum of digits (16).

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (48407) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 8 ways as a sum of consecutive naturals, for example, 4395 + ... + 4405.

2⁴⁸⁴⁰⁰ is an apocalyptic number.

48400 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

48400 is the 220-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 48400

48400 is an abundant number, since it is smaller than the sum of its proper divisors (79413).

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

48400 is a wasteful number, since it uses less digits than its factorization.

48400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 40 (or 18 counting only the distinct ones).

The product of its (nonzero) digits is 128, while the sum is 16.

The cubic root of 48400 is about 36.4430838719.

Subtracting from 48400 its sum of digits (16), we obtain a palindrome (48384).

Multiplying 48400 by its sum of digits (16), we get a square (774400 = 880²).

48400 divided by its sum of digits (16) gives a square (3025 = 55²).

Adding to 48400 its reverse (484), we get a palindrome (48884).

Multiplying 48400 by its reverse (484), we get a square (23425600 = 4840²).

48400 divided by its reverse (484) gives a square (100 = 10²).

The spelling of 48400 in words is "forty-eight thousand, four hundred".