About the Number 360360 (three hundred sixty thousand three hundred sixty)

MathBabbler learned that the number 2520 was the smallest number that had the number 1 through 10 as proper divisors. A progam was writte to print the smallest numbers that have proper divisors 1-3, 1-4, 1-5, and so on to 1-24. The number 360,360 is the smallest number that has 1-13, 1-14 and 1-15 as proper divisors.

MathBabbler Number Analyst (MBNA) output:
=========================================
360360 is a natural, whole, integer
360360 is even
360360 proper divisors are: 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,18,
                            20,21,22,24,26,28,30,33,35,36,39,40,42,
                            44,45,52,55,56,60,63,65,66,70,72,77,78,
                            84,88,90,91,99,104,105,110,117,120,126,
                            130,132,140,143,154,156,165,168,180,182,
                            195,198,210,220,231,234,252,260,264,273,
                            280,286,308,312,315,330,360,364,385,390,
                            396,420,429,440,455,462,468,495,504,520,
                            546,572,585,616,630,660,693,715,728,770,
                            780,792,819,840,858,910,924,936,990,1001,
                            1092,1144,1155,1170,1260,1287,1320,1365,
                            1386,1430,1540,1560,1638,1716,1820,1848,
                            1980,2002,2145,2184,2310,2340,2520,2574,
                            2730,2772,2860,3003,3080,3276,3432,3465,
                            3640,3960,4004,4095,4290,4620,4680,5005,
                            5148,5460,5544,5720,6006,6435,6552,6930,
                            8008,8190,8580,9009,9240,10010,10296,
                            10920,12012,12870,13860,15015,16380,17160,
                            18018,20020,24024,25740,27720,30030,32760,
                            36036,40040,45045,51480,60060,72072,90090,
                            120120,180180 
360360 has 191 proper divisors
360360 is abundant (sum of divisors is 1212120; ratio: 3.36364)
360360 is unhappy
360360 is a Harshad number
360360 is not prime
360360 has the prime factors: 2*2*2*3*3*5*7*11*13 (sum=48)
2...2...2...3...3...5...7...11...13...answer: 48
360360 in octal is 01277650
360360 in hexadecimal is 0x57fa8
360360 in binary is 1010111111110101000 (is evil)
360360 nearest square numbers: -360...841 (360000...361201 [601])
sqrt(360360) = 600.3
ln(360360) = 12.7949
log(360360) = 5.55674
360360 reciprocal is .00000277500277500277500277500277
360360 is an apocalyptic power
360360! is inf
360360 is 114706 Pi years
360360 is 18018 scoreyears
360360 = 90091^2 - 90089^2 and 2 * (90091 + 90089) = 360360

Creator: Gerald Thurman [gthurman@gmail.com]
Created: 19 November 2013 (posted 22 November 2013)

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This work is licensed under a Creative Commons Attribution 3.0 United States License.