## A Multiplication Based Logic Puzzle

### 663 Peanut Butter Kiss Puzzle

It’s easy to see that 663 is divisible by three.

That may not be very interesting at all, but…..

Because 13 and 17, 663’s other two prime factors, have a remainder of one when each is divided by four, 663 is the hypotenuse of FOUR Pythagorean triples. Can you find the greatest common factor of each triple?

• 420-513-663
• 63-660-663
• 255-612-663
• 312-585-663

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Art is not one of my strongest skills, but here is my attempt to make a puzzle that looks like a peanut butter kiss, a traditional Halloween candy:

Color can be inviting, but it can also be distracting. Here is the same puzzle without the added color:

Print the puzzles or type the solution on this excel file: 10 Factors 2015-10-26

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• 663 is a composite number.
• Prime factorization: 663 = 3 x 13 x 17
• 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 663 has exactly 8 factors.
• Factors of 663: 1, 3, 13, 17, 39, 51, 221, 663
• Factor pairs: 663 = 1 x 663, 3 x 221, 13 x 51, or 17 x 39
• 663 has no square factors that allow its square root to be simplified. √663 ≈ 25.748786.

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Thank you for sharing the solution, Ricardo, and happy Halloween: