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205920 = 253251113
BaseRepresentation
bin110010010001100000
3101110110200
4302101200
523042140
64225200
71515231
oct622140
9343420
10205920
11130790
129b200
1372960
1455088
1541030
hex32460

205920 has 144 divisors (see below), whose sum is σ = 825552. Its totient is φ = 46080.

The previous prime is 205913. The next prime is 205937. The reversal of 205920 is 29502.

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 a junction number, because it is equal to n+sod(n) for n = 205893 and 205902.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 205920.

It is an unprimeable number.

205920 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, 15834 + ... + 15846.

It is an arithmetic number, because the mean of its divisors is an integer number (5733).

2205920 is an apocalyptic number.

205920 is a gapful number since it is divisible by the number (20) 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 205920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (412776).

205920 is an abundant number, since it is smaller than the sum of its proper divisors (619632).

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

205920 is a wasteful number, since it uses less digits than its factorization.

205920 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 45 (or 34 counting only the distinct ones).

The product of its (nonzero) digits is 180, while the sum is 18.

The square root of 205920 is about 453.7840896285. The cubic root of 205920 is about 59.0517596158.

The spelling of 205920 in words is "two hundred five thousand, nine hundred twenty".

Divisors: 1 2 3 4 5 6 8 9 10 11 12 13 15 16 18 20 22 24 26 30 32 33 36 39 40 44 45 48 52 55 60 65 66 72 78 80 88 90 96 99 104 110 117 120 130 132 143 144 156 160 165 176 180 195 198 208 220 234 240 260 264 286 288 312 330 352 360 390 396 416 429 440 468 480 495 520 528 572 585 624 660 715 720 780 792 858 880 936 990 1040 1056 1144 1170 1248 1287 1320 1430 1440 1560 1584 1716 1760 1872 1980 2080 2145 2288 2340 2574 2640 2860 3120 3168 3432 3744 3960 4290 4576 4680 5148 5280 5720 6240 6435 6864 7920 8580 9360 10296 11440 12870 13728 15840 17160 18720 20592 22880 25740 34320 41184 51480 68640 102960 205920