# 1658 Mystery Puzzle

Contents

### Today’s Puzzle:

What’s the mystery?
Will the common factor of 30 and 20 be 5 or 10?
Will the common factor of 36 and 18 be 6 or 9?
Will the common factor of 60 and 30 be 6 or 10? and
Will the common factor of 8 and 16 be 2, 4, or 8?

Don’t guess which common factors to use! Look at all the clues. They work together to help you logically arrive at the puzzle’s unique solution. ### Factors of 1658:

• 1658 is a composite number.
• Prime factorization: 1658 = 2 × 829.
• 1658 has no exponents greater than 1 in its prime factorization, so √1658 cannot be simplified.
• The exponents in the prime factorization are 1 and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 1658 has exactly 4 factors.
• The factors of 1658 are outlined with their factor pair partners in the graphic below. ### More About the Number 1658:

1658 is the sum of two squares:
37² + 17² = 1658.

1658 is the hypotenuse of a Pythagorean triple:
1080-1258-1658, which is 2 times (540-629-829),
and can also be calculated from 37² – 17², 2(37)(17), 37² + 17².

1658 is also a leg in the Pythagorean triple
calculated from 2(829), 829² – 1², 829² + 1².

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