1514 and Level 2

Today’s Puzzle:

There is only one way to write the factors from 1 to 12 in both the first column and the top row so that this puzzle will behave like a multiplication table. The given clues will be the products of the factors you write. Can you find the way?

Factors of 1514:

  • 1514 is a composite number.
  • Prime factorization: 1514 = 2 × 757
  • 1514 has no exponents greater than 1 in its prime factorization, so √1514 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 1514 has exactly 4 factors.
  • The factors of 1514 are outlined with their factor pair partners in the graphic below.

More Facts about the number 1514:

1514 is the sum of two squares:
35² + 17² = 1514

1514 is the hypotenuse of a Pythagorean triple:
936-1190-1514 calculated from 35² – 17², 2(35)(17), 35² + 17²