# 940 Mystery Level

Today’s puzzle reminds me of a gumball machine. I would invite you to stick to solving this puzzle until you find success. I assure you that the factors from 1 to 10 can be placed in the first column and the top row solely by using logic.

Print the puzzles or type the solution on this excel file: 10-factors-932-941

Now let me tell you something about the number 940.

940 is the hypotenuse of a Pythagorean triple:
564-752-940 which is (3-4-5) times 188

• 940 is a composite number.
• Prime factorization: 940 = 2 × 2 × 5 × 47, which can be written 940 = 2² × 5 × 47
• The exponents in the prime factorization are 2, 1, and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1)(1 + 1) = 3 × 2 × 2 = 12. Therefore 940 has exactly 12 factors.
• Factors of 940: 1, 2, 4, 5, 10, 20, 47, 94, 188, 235, 470, 940
• Factor pairs: 940 = 1 × 940, 2 × 470, 4 × 235, 5 × 188, 10 × 94, or 20 × 47,
• Taking the factor pair with the largest square number factor, we get √940 = (√4)(√235) = 2√235 ≈ 30.659419