# 1254 and Level 3

Find the common factor of 8 and 80 so that only numbers from 1 to 12 will be put in the top row of this multiplication table puzzle. Then work down row by row writing the factors of each clue so that the numbers from 1 to 12 appear only once in both the first column and the top row. You can do this! Print the puzzles or type the solution in this excel file: 12 factors 1251-1258

Here are a few facts about the post number, 1254:

• 1254 is a composite number.
• Prime factorization: 1254 = 2 × 3 × 11 × 19
• The exponents in the prime factorization are 1, 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 × 2 = 16. Therefore 1254 has exactly 16 factors.
• Factors of 1254: 1, 2, 3, 6, 11, 19, 22, 33, 38, 57, 66, 114, 209, 418, 627, 1254
• Factor pairs: 1254 = 1 × 1254, 2 × 627, 3 × 418, 6 × 209, 11 × 114, 19 × 66, 22 × 57, or 33 × 38
• 1254 has no square factors that allow its square root to be simplified. √1254 ≈ 35.41186 1254 is the sum of the twenty-four prime numbers from 7 to 103. Do you know what those prime numbers are?

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