# 1233 and Level 1

Perhaps this puzzle is as difficult as a level 1 puzzle can be, but it is still not all that difficult. Nevertheless, if you can solve it, give yourself a big pat on the back. Print the puzzles or type the solution in this excel file: 12 factors 1232-1241

Here are a few facts about the number 1233:

• 1233 is a composite number.
• Prime factorization: 1233 = 3 × 3 × 137, which can be written 1233 = 3² × 137
• The exponents in the prime factorization are 2 and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1) = 3 × 2  = 6. Therefore 1233 has exactly 6 factors.
• Factors of 1233: 1, 3, 9, 137, 411, 1233
• Factor pairs: 1233 = 1 × 1233, 3 × 411, or 9 × 137
• Taking the factor pair with the largest square number factor, we get √1233 = (√9)(√137) = 3√137 ≈ 35.1141 Look at the numbers in this very cool but square fact about 1233:
12² + 33² = 1233

1233 is the hypotenuse of a Pythagorean triple:
792-945-1233 calculated from 2(33)(12), 33² – 12², 33² + 12²
It is also 9 times (88-105-137)

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