## A Multiplication Based Logic Puzzle

### 296 and Level 1

• 296 is a composite number.
• Prime factorization: 296 = 2 x 2 x 2 x 37 which can be written 296 = 2³ x 37
• The exponents in the prime factorization are 3 and 1. Adding one to each and multiplying we get (3 + 1)(1 + 1) = 4 x 2 = 8. Therefore 296 has exactly 8 factors.
• Factors of 296: 1, 2, 4, 8, 37, 74, 148, 296
• Factor pairs: 296 = 1 x 296, 2 x 148, 4 x 74, or 8 x 37
• Taking the factor pair with the largest square number factor, we get √296 = (√4)(√74) = 2√74 ≈ 17.2046505

Although I came home from the hospital on Sunday, I haven’t felt like spending much time on the computer reading or writing anything. Full recovery will be another five weeks, but hopefully I’ll start feeling better in less time.  I do feel better today than I did on Sunday.

Print the puzzles or type the factors on this excel file: 12 Factors 2014-11-17

#### Comments on: "296 and Level 1" (3)

1. Welcome back. Very best wishes, Alan

Liked by 1 person

2. So sorry to hear that you are ill. I hope you make a speedy and full recovery!

Liked by 1 person

3. Glad to see you back. 296, with 8 factors! …seems like a great number to come back with. Be well.

Liked by 1 person