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468000 = 25325313
BaseRepresentation
bin1110010010000100000
3212202222100
41302100200
5104434000
614010400
73656301
oct1622040
9782870
10468000
1129a685
121a6a00
13135030
14c27a8
1593a00
hex72420

468000 has 144 divisors (see below), whose sum is σ = 1788696. Its totient is φ = 115200.

The previous prime is 467977. The next prime is 468001. The reversal of 468000 is 864.

It can be written as a sum of positive squares in 4 ways, for example, as 63504 + 404496 = 252^2 + 636^2 .

It is a tau number, because it is divible by the number of its divisors (144).

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

It is not an unprimeable number, because it can be changed into a prime (468001) by changing a digit.

468000 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 23 ways as a sum of consecutive naturals, for example, 35994 + ... + 36006.

2468000 is an apocalyptic number.

468000 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 468000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (894348).

468000 is an abundant number, since it is smaller than the sum of its proper divisors (1320696).

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

468000 is a wasteful number, since it uses less digits than its factorization.

468000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 44 (or 23 counting only the distinct ones).

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

The square root of 468000 is about 684.1052550595. The cubic root of 468000 is about 77.6393607666.

Adding to 468000 its reverse (864), we get a palindrome (468864).

The spelling of 468000 in words is "four hundred sixty-eight thousand".

Divisors: 1 2 3 4 5 6 8 9 10 12 13 15 16 18 20 24 25 26 30 32 36 39 40 45 48 50 52 60 65 72 75 78 80 90 96 100 104 117 120 125 130 144 150 156 160 180 195 200 208 225 234 240 250 260 288 300 312 325 360 375 390 400 416 450 468 480 500 520 585 600 624 650 720 750 780 800 900 936 975 1000 1040 1125 1170 1200 1248 1300 1440 1500 1560 1625 1800 1872 1950 2000 2080 2250 2340 2400 2600 2925 3000 3120 3250 3600 3744 3900 4000 4500 4680 4875 5200 5850 6000 6240 6500 7200 7800 9000 9360 9750 10400 11700 12000 13000 14625 15600 18000 18720 19500 23400 26000 29250 31200 36000 39000 46800 52000 58500 78000 93600 117000 156000 234000 468000