48384 has 72 divisors (see below), whose sum is σ = 163520. Its totient is φ = 13824.

The previous prime is 48383. The next prime is 48397.

48384 is nontrivially palindromic in base 10.

It is a tau number, because it is divible by the number of its divisors (72).

It is a super-2 number, since 2×48384^{2} = 4682022912, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a nude number because it is divisible by every one of its digits.

It is an Ulam number.

Its product of digits (3072) is a multiple of the sum of its prime divisors (12).

It is a nialpdrome in base 9.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (48383) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 6909 + ... + 6915.

2^{48384} is an apocalyptic number.

48384 is a droll number since its even prime factors and its odd prime factors have the same sum.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 48384, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (81760).

48384 is an abundant number, since it is smaller than the sum of its proper divisors (115136).

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

48384 is an equidigital number, since it uses as much as digits as its factorization.

48384 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 32 (or 12 counting only the distinct ones).

The product of its digits is 3072, while the sum is 27.

The square root of 48384 is about 219.9636333579. The cubic root of 48384 is about 36.4390676625.

The spelling of 48384 in words is "forty-eight thousand, three hundred eighty-four".

Divisors: 1 2 3 4 6 7 8 9 12 14 16 18 21 24 27 28 32 36 42 48 54 56 63 64 72 84 96 108 112 126 128 144 168 189 192 216 224 252 256 288 336 378 384 432 448 504 576 672 756 768 864 896 1008 1152 1344 1512 1728 1792 2016 2304 2688 3024 3456 4032 5376 6048 6912 8064 12096 16128 24192 48384

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