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Today’s Puzzle:
Factors of 1788:
A factor tree for 1788 isn’t very big because one of its prime factors has 3 digits.
- 1788 is a composite number.
- Prime factorization: 1788 = 2 × 2 × 3 × 149, which can be written 1788 = 2² × 3 × 149.
- 1788 has at least one exponent greater than 1 in its prime factorization so √1788 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1788 = (√4)(√447) = 2√447.
- The exponents in the prime factorization are 2, 1, and 1. Adding one to each exponent and multiplying we get (2 + 1)(1 + 1)(1 + 1) = 3 × 2 × 2 = 12. Therefore 1788 has exactly 12 factors.
- The factors of 1788 are outlined with their factor pair partners in the graphic below.
More About the Number 1788:
1788 is the hypotenuse of a Pythagorean triple:
612-1680-1788 which is 12 times (51-140-149).
1788 is the difference of two squares in two different ways:
448² – 446² = 1788, and
152² – 146² = 1788.
Two more square facts about 1788:
227² – 226² + 225² – 224² + 223² – 222² + 221² – 220² = 1788.
86² – 85² + 84² – 83² + 82² – 81² + 80² – 79² + 78² – 77² + 76² – 75² + 74² – 73² + 72² – 71² + 70² – 69² + 68² – 67² + 66² – 65² + 64² – 63² = 1788.