460800 has 108 divisors (see below), whose sum is σ = 1650285. Its totient is φ = 122880.

The previous prime is 460793. The next prime is 460813. The reversal of 460800 is 8064.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

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

It can be written as a sum of positive squares in 2 ways, for example, as 451584 + 9216 = 672^2 + 96^2 .

It is an ABA number since it can be written as A⋅B^{A}, here for A=2, B=480.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is an Ulam number.

It is an unprimeable number.

460800 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 8 ways as a sum of consecutive naturals, for example, 92158 + ... + 92162.

2^{460800} is an apocalyptic number.

460800 is a gapful number since it is divisible by the number (40) 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 460800

460800 is an abundant number, since it is smaller than the sum of its proper divisors (1189485).

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

460800 is a wasteful number, since it uses less digits than its factorization.

460800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 38 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 192, while the sum is 18.

The square root of 460800 is about 678.8225099391. The cubic root of 460800 is about 77.2391507685.

Multiplying 460800 by its sum of digits (18), we get a square (8294400 = 2880^{2}).

460800 divided by its sum of digits (18) gives a square (25600 = 160^{2}).

Adding to 460800 its reverse (8064), we get a palindrome (468864).

The spelling of 460800 in words is "four hundred sixty thousand, eight 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 2048 2304 2400 2560 2880 3072 3200 3600 3840 4608 4800 5120 5760 6144 6400 7200 7680 9216 9600 10240 11520 12800 14400 15360 18432 19200 23040 25600 28800 30720 38400 46080 51200 57600 76800 92160 115200 153600 230400 460800

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