• 231 is a composite number and a triangular number.
• Prime factorization: 231 = 3 x 7 x 11
• The exponents in the prime factorization are 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 x 2 x 2 = 8. Therefore 231 has 8 factors.
• Factors of 231: 1, 3, 7, 11, 21, 33, 77, 231
• Factor pairs: 231 = 1 x 231, 3 x 77, 7 x 33, or 11 x 21
• 231 has no square factors so its square root cannot be simplified. √231 ≈ 15.199

• Because 21 + 1 = 22 and 21 x (22/2) = 231, we know 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 = 231

Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-09-08