### About the Number 7,272 (seven thousand two hundred seventy-two)

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 number
```

MathBabbler couldn't remember what made a number a Kaprekar number, so he looked at the nBAB collection of Kaprekar numbers and discovered that 7272 is a Kaprekar number.

```   square 7272:  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 = 7272
```

Note: The MBNA (MathBabbler Number Analyst) starting checking for Kaprekar numbers on 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 )
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 