About the Number 126 (one hundred twenty-six)

MathBabbler created a nBAB for the number 125 on 29 March 2009. While working on that nBAB, he learned that 125 was a Ruth-Aaron pair with 126. On 31 March 2009, MathBabbler and his CSC100 class wrote a C program that determines if a number is a member of the Ruth-Aaron pair. This nBAB about the number 126 was the second nBAB to use the MBNA's Ruth-Aaron program.

   MathBabbler Number Analyst (MBNA) output:
   =========================================
   126 is a natural, whole, integer
   126 is even
   126 proper divisors are: 1,2,3,6,7,9,14,18,21,42,63,
   126 is abundant (sum of divisors is 186)
   126 is unhappy
   126 is a Harshad number
   126 is not prime
   126 has the prime factors: 2*3*3*7
   126 sum prime factors: 2...3...3...7...answer: 15
   126 and 125 are a Ruth-Aaron pair
   126 in octal is 0176
   126 in hexadecimal is 0x7e
   126 in binary is 1111110 (is evil)
   126 nearest square numbers: -5...18 (121...144 [12])
   sqrt(126) = 11.225
   ln(126) = 4.83628
   log(126) = 2.10037
   126 reciprocal is .00793650793650793650793650793650
   126! is 2.37217e+211
   126 is 40.107 Pi years
   126 is 6 score and 6 years
   126 written as a Roman numeral is CXXVI

[Wikipedia] 126 is a Friedman number because it is an integer which, in base-10, is the "result of an expression using all its own digits in combination with any of the four basic arithmetic operators and sometimes exponentiation."

   126 = 6 * 21

Observe...

   sqrt(126) / (ln(126) + log(126)) = 1.6182117

1.6182117 minus Phi is 0.000177711762; in other words, the square-root of 126 divided-by the natural log of 126 plus the common log of 126 approximates the Golden Ratio.


Creator: Gerald Thurman [gthurman@gmail.com]
Created: 02 April 2009

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