# 1334 and Level 2

You only need a few clues in the right places to figure out where all the factors from 1 to 12 belong in this mixed up multiplication table puzzle. You can use those clues to put the factors in the right places and solve this one! Print the puzzles or type the solution in this excel file: 12 factors 1333-1341

• 1334 is a composite number.
• Prime factorization: 1334 = 2 × 23 × 29
• 1334 has no exponents greater than 1 in its prime factorization, so √1334 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 1334 has exactly 8 factors.
• The factors of 1334 are outlined with their factor pairs in the graphic below. 1334 is the hypotenuse of a Pythagorean triple:
920-966-1334 which is (20-21-29) times 46

It is also the leg in a couple of triples:
312-1334-1370 calculated from 29² – 23², 2(29)(23), 29² + 23²
1334-444888-444890 calculated from 2(667)(1). 667² – 1² , 667² + 1²