1455 and Level 1

Today’s Puzzle:

All of the clues in today’s puzzle are divisible by the same number. Can you figure out what that number is? If you can, then you can solve this puzzle.

Factors of 1455:

That was puzzle number 1455. In case you would like to know a little bit about that number, here are a few facts:

  • 1455 is a composite number.
  • Prime factorization: 1455 = 3 × 5 × 97
  • 1455 has no exponents greater than 1 in its prime factorization, so √1455 cannot be simplified.
  • The exponents in the prime factorization are 1, 1, and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 = 8. Therefore 1455 has exactly 8 factors.
  • The factors of 1455 are outlined with their factor pair partners in the graphic below.

Facts about the number 1455:

1455 is the difference of two squares in four different ways:
728² – 727² = 1455
244² – 241² = 1455
148² – 143² = 1455
56² – 41² = 1455

1455 is also the hypotenuse of four Pythagorean triples:
132-1449-1455 which is 3 times (44-483-485)
279-1428-1455 which is 3 times (93-476-485)
873-1164-1455 which is (3-4-5) times 291
975-1080-1455 which is 15 times (65-72-97)

 

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