1502 and Level 1

Today’s Puzzle:

This level 1 puzzle has products in one of the rows and in one of the columns. Can you use those products to figure out where the factors 1 to 10 belong in this multiplication table puzzle?

Factors of 1502:

  • 1502 is a composite number.
  • Prime factorization: 1502 = 2 × 751
  • 1502 has no exponents greater than 1 in its prime factorization, so √1502 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 1502 has exactly 4 factors.
  • The factors of 1502 are outlined with their factor pair partners in the graphic below.

Pythagorean Triple with 1502:

1502 is not the sum or the difference of two squares, but 1502 = 2(751)(1), so it is part of a Pythagorean triple:
1502-564000-564002, calculated from 2(751)(1), 751² – 1², 751² – 1².

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