4 + 2 + 3 = 9 therefore 423 can be evenly divided by both 3 and 9. Thus we know right away that it is a composite number whose square root can be simplified.

Also ANY natural number ending in 24 or 25 has a reducible square root, so with 423, 424, and 425 we have THREE consecutive numbers with reducible square roots. Sadly, 426 breaks the pattern so we do not have a fourth.

Print the puzzles or type the factors on this excel file: 12 Factors 2015-03-09

• 423 is a composite number.
• Prime factorization: 423 = 3 x 3 x 47, which can be written 423 = (3^2) x 47
• The exponents in the prime factorization are 2 and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1) = 3 x 2  = 6. Therefore 423 has exactly 6 factors.
• Factors of 423: 1, 3, 9, 47, 141, 423
• Factor pairs: 423 = 1 x 423, 3 x 141, or 9 x 47
• Taking the factor pair with the largest square number factor, we get √423 = (√9)(√47) = 3√47 ≈ 20.5670