# 1083 and Level 3

Start with the two clues near the top of this level 3 puzzle. Find their common factor that will put only numbers from 1 to 12 in the top row. Then work down the puzzle row by row filling in factors from 1 to 12 as you go. It won’t take you long to complete this puzzle! Print the puzzles or type the solution in this excel file: 12 factors 1080-1086

1 + 0 + 8 + 3 = 12, so 1083 can be evenly divided by 3. What else can I tell you about that number?

• 1083 is a composite number.
• Prime factorization: 1083 = 3 × 19 × 19, which can be written 1083 = 3 × 19²
• The exponents in the prime factorization are 1 and 2. Adding one to each and multiplying we get (1 + 1)(2 + 1) = 2 × 3  = 6. Therefore 1083 has exactly 6 factors.
• Factors of 1083: 1, 3, 19, 57, 361, 1083
• Factor pairs: 1083 = 1 × 1083, 3 × 361, or 19 × 57
• Taking the factor pair with the largest square number factor, we get √1083 = (√361)(√3) = 19√3 ≈ 32.90897 1083 looks interesting when it is written in some other bases:
It’s 575 in BASE 14 because 5(14²) + 7(14) + 5(1) = 1083,
363 in BASE 18 because 3(18²) + 6(18) + 3(1) = 3(18² + 36 + 1) = 3(361) = 1083,
300 in BASE 19 because 3(19²) = 1083, and
it’s 212 in BASE 23 because 2(23²) + 1(23) + 2(1) = 1083