1325 Hockey Stick

 

If someone you know loves hockey and wants a fun way to practice multiplication facts, this hockey stick could be the perfect gift.

Print the puzzles or type the solution in this excel file:10-factors-1321-1332

  • 1325 is a composite number.
  • Prime factorization: 1325 = 5 × 5 × 53, which can be written 1325 = 5² × 53
  • The exponents in the prime factorization are 2 and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1) = 3 × 2  = 6. Therefore 1325 has exactly 6 factors.
  • Factors of 1325: 1, 5, 25, 53, 265, 1325
  • Factor pairs: 1325 = 1 × 1325, 5 × 265, or 25 × 53
  • Taking the factor pair with the largest square number factor, we get √1325 = (√25)(√53) = 5√53 ≈ 36.40055

1325 is the sum of two squares in three different ways:
29² + 22² = 1325 
34² + 13² = 1325
35² + 10² = 1325

1325 is the hypotenuse of SEVEN Pythagorean triples:
115-1320-1325 which is 5 times (23-264-265)
357-1276-1325 calculated from 29² – 22², 2(29)(22), 29² + 22²
371-1272-1325 which is (7-24-25) times 53
480-1235-1325 which is 5 times (96-247-265)
700-1125-1325 calculated from 2(35)(10), 35² – 10², 35² + 10²
795-1060-1325 which is (3-4-5) times 265
884-987-1325 calculated from 2(34)(13), 34² – 13², 34² + 13²

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