38400 has 60 divisors (see below), whose sum is σ = 126852. Its totient is φ = 10240.

The previous prime is 38393. The next prime is 38431. The reversal of 38400 is 483.

Multipling 38400 by its product of nonzero digits (96), we get a square (3686400 = 1920^{2}).

38400 divided by its product of nonzero digits (96) gives a square (400 = 20^{2}).

Adding to 38400 its reverse (483), we get a palindrome (38883).

It can be divided in two parts, 3 and 8400, that multiplied together give a triangular number (25200 = T_{224}).

It is a tau number, because it is divible by the number of its divisors (60).

It is a Harshad number since it is a multiple of its sum of digits (15).

It is a nialpdrome in base 14 and base 16.

It is a zygodrome in base 14.

It is a self number, because there is not a number *n* which added to its sum of digits gives 38400.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 7678 + ... + 7682.

2^{38400} is an apocalyptic number.

38400 is a gapful number since it is divisible by the number (30) 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 38400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (63426).

38400 is an abundant number, since it is smaller than the sum of its proper divisors (88452).

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

38400 is an equidigital number, since it uses as much as digits as its factorization.

38400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 31 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 96, while the sum is 15.

The square root of 38400 is about 195.9591794227. The cubic root of 38400 is about 33.7373066121.

The spelling of 38400 in words is "thirty-eight thousand, four hundred".

Divisors: 1 2 3 4 5 6 8 10 12 15 16 20 24 25 30 32 40 48 50 60 64 75 80 96 100 120 128 150 160 192 200 240 256 300 320 384 400 480 512 600 640 768 800 960 1200 1280 1536 1600 1920 2400 2560 3200 3840 4800 6400 7680 9600 12800 19200 38400

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