230400 has 99 divisors (see below), whose sum is σ = 824941. Its totient is φ = 61440.

The previous prime is 230393. The next prime is 230431. The reversal of 230400 is 4032.

Adding to 230400 its reverse (4032), we get a palindrome (234432).

It can be divided in two parts, 230 and 400, that added together give a triangular number (630 = T_{35}).

230400 = T_{479} + T_{480}.

The square root of 230400 is 480.

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

It is a Jordan-Polya number, since it can be written as (5!)^{2} ⋅ (2!)^{4}.

It can be written as a sum of positive squares in only one way, i.e., 82944 + 147456 = 288^2 + 384^2 .

It is a Harshad number since it is a multiple of its sum of digits (9).

It is a Duffinian number.

It is an unprimeable number.

It is a polite number, since it can be written in 8 ways as a sum of consecutive naturals, for example, 46078 + ... + 46082.

2^{230400} is an apocalyptic number.

230400 is a gapful number since it is divisible by the number (20) formed by its first and last digit.

230400 is the 480-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 230400

230400 is an abundant number, since it is smaller than the sum of its proper divisors (594541).

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

230400 is a wasteful number, since it uses less digits than its factorization.

230400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 36 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 24, while the sum is 9.

The cubic root of 230400 is about 61.3047545915.

The spelling of 230400 in words is "two hundred thirty thousand, four hundred".

Divisors: 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 30 32 36 40 45 48 50 60 64 72 75 80 90 96 100 120 128 144 150 160 180 192 200 225 240 256 288 300 320 360 384 400 450 480 512 576 600 640 720 768 800 900 960 1024 1152 1200 1280 1440 1536 1600 1800 1920 2304 2400 2560 2880 3072 3200 3600 3840 4608 4800 5120 5760 6400 7200 7680 9216 9600 11520 12800 14400 15360 19200 23040 25600 28800 38400 46080 57600 76800 115200 230400

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