MathBabbler was looking at Stetson.edu::What's Special About This Number? and he noticed that the number 45 was a

Kaprekar number.Definition for a

Kaprekar number.1 is a Kaprekar number otherwise, square the number if resulting product has a even number of digits, split the product into two separate numbers if sum equals number, then Kaprekar numberMathBabbler couldn't remember what made a number a

Kaprekar number, so he looked at the nBAB collection ofKaprekar numbersand discovered that7272is aKaprekar number.square7272:7272^2 = 52881984 52881984 has an even number of digits (8) split 52881984 into two 4-digit numbers: 5288|1984 sum the two 4-digit numbers: 5288 + 1984 =7272Note: The MBNA (MathBabbler Number Analyst) starting checking for

Kaprekar numberson 1 June 2012.MathBabbler Number Analyst (MBNA) output: ========================================= 7272 is a natural, whole, integer 7272 is even 7272 proper divisors are: 1,2,3,4,6,8,9,12,18,24,36,72,101,202, 303,404,606,808,909,1212,1818,2424,3636, 7272 is refactorable (evenly divisable by # of divisors) 7272 has 23 proper divisors 7272 is abundant (sum of divisors is 12618; ratio: 1.73515) 7272 is unhappy 7272 is not a Squarefree Number: 4,9,36, 7272 is Harshad (Niven) number 7272 is composite (not prime) 7272 has the prime factors: 2*2*2*3*3*101 (sum=113) 7272 is undulating 7272 is Kaprekar number 7272 is the sum of 28 consecutive primes 7272 = 181 + 191 + 193 + 197 + 199 + 211 + 223 + 227 + 229 + 233 + 239 + 241 + 251 + 257 + 263 + 269 + 271 + 277 + 281 + 283 + 293 + 307 + 311 + 313 + 317 + 331 + 337 + 347 7272 in octal is 016150 7272 in hexadecimal is 0x1c68 7272 in binary is 1110001101000 (is evil) 7272 nearest square numbers: -47...124 (7225...7396 [86]) sqrt(7272) = 85.276 ln(7272) = 8.89179 log(7272) = 3.86165 7272 reciprocal is .00013751375137513751375137513751 7272 is an apocalyptic power 7272! is inf 7272 is 2314.75 Pi years 7272 is 363 score and 12 years 7272 is 1819^2 - 1817^2 and 2 * (1819 + 1817) 7272 is a multiple of 2 & it contains a 2 (A121022) 7272 is a multiple of 72 & it contains a 72

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

**Created:** 19 January 2015

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