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

360,360is 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)

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