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

720,720is the smallest number that has 1-16 as proper divisors.MathBabbler Number Analyst (MBNA) output: ========================================= 720720 is a natural, whole, integer 720720 is even 720720 proper divisors are: 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18, 20,21,22,24,26,28,30,33,35,36,39,40,42,44, 45,48,52,55,56,60,63,65,66,70,72,77,78,80, 84,88,90,91,99,104,105,110,112,117,120,126, 130,132,140,143,144,154,156,165,168,176,180, 182,195,198,208,210,220,231,234,240,252,260, 264,273,280,286,308,312,315,330,336,360,364, 385,390,396,420,429,440,455,462,468,495,504, 520,528,546,560,572,585,616,624,630,660,693, 715,720,728,770,780,792,819,840,858,880,910, 924,936,990,1001,1008,1040,1092,1144,1155,1170, 1232,1260,1287,1320,1365,1386,1430,1456,1540,1560, 1584,1638,1680,1716,1820,1848,1872,1980,2002,2145, 2184,2288,2310,2340,2520,2574,2640,2730,2772,2860, 3003,3080,3120,3276,3432,3465,3640,3696,3960,4004, 4095,4290,4368,4620,4680,5005,5040,5148,5460,5544, 5720,6006,6160,6435,6552,6864,6930,7280,7920,8008, 8190,8580,9009,9240,9360,10010,10296,10920,11088, 11440,12012,12870,13104,13860,15015,16016,16380, 17160,18018,18480,20020,20592,21840,24024,25740, 27720,30030,32760,34320,36036,40040,45045,48048, 51480,55440,60060,65520,72072,80080,90090,102960, 120120,144144,180180,240240,360360, 720720 is refactorable (evenly divisable by # of divisors) 720720 has 239 proper divisors 720720 is abundant (sum of divisors is 2529072; ratio: 3.50909) 720720 is unhappy 720720 is a Harshad number 720720 is not prime 720720 has the prime factors: 2*2*2*2*3*3*5*7*11*13 (sum=50) 2...2...2...2...3...3...5...7...11...13...answer: 50 720720 in octal is 02577520 720720 in hexadecimal is 0xaff50 720720 in binary is 10101111111101010000 (is evil) 720720 nearest square numbers: -1616...81 (719104...720801 [849]) sqrt(720720) = 848.952 ln(720720) = 13.488 log(720720) = 5.85777 720720 reciprocal is .00000138750138750138750138750138 720720 is an apocalyptic power 720720! is inf 720720 is 229412 Pi years 720720 is 36036 scoreyears 720720 = 180181^2 - 180179^2 and 2 * (180181 + 180179) = 720720

**Creator:** Gerald Thurman
[gthurman@gmail.com]

**Created:** 23 November 2013 (posted 25 November 2013)

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