16400 has 30 divisors (see below), whose sum is σ = 40362. Its totient is φ = 6400.

The previous prime is 16381. The next prime is 16411. The reversal of 16400 is 461.

Adding to 16400 its reverse (461), we get a palindrome (16861).

It can be divided in two parts, 16 and 400, that multiplied together give a square (6400 = 80^{2}).

16400 = T_{23} + T_{24} + ... +
T_{47}.

16400 is nontrivially palindromic in base 9.

It can be written as a sum of positive squares in 3 ways, for example, as 16 + 16384 = 4^2 + 128^2 .

It is a plaindrome in base 11.

It is a congruent number.

It is an unprimeable number.

16400 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 (2) of ones.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 380 + ... + 420.

It is the magic constant of a 32 × 32 magic square.

2^{16400} is an apocalyptic number.

16400 is a gapful number since it is divisible by the number (10) 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 16400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (20181).

16400 is an abundant number, since it is smaller than the sum of its proper divisors (23962).

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

16400 is a wasteful number, since it uses less digits than its factorization.

16400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 59 (or 48 counting only the distinct ones).

The product of its (nonzero) digits is 24, while the sum is 11.

The square root of 16400 is about 128.0624847487. The cubic root of 16400 is about 25.4066818554.

The spelling of 16400 in words is "sixteen thousand, four hundred".

Divisors: 1 2 4 5 8 10 16 20 25 40 41 50 80 82 100 164 200 205 328 400 410 656 820 1025 1640 2050 3280 4100 8200 16400

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