# 248 and Level 3

• 248 is a composite number.
• Prime factorization: 248 = 2 x 2 x 2 x 31, which can be written 248 = (2^3) x 31
• The exponents in the prime factorization are 3, and 1. Adding one to each and multiplying we get (3 + 1)(1 + 1) = 4 x 2 = 8. Therefore 248 has 8 factors.
• Factors of 248: 1, 2, 4, 8, 31, 62, 124, 248
• Factor pairs: 248 = 1 x 248, 2 x 124, 4 x 62, or 8 x 31
• Taking the factor pair with the largest square number factor, we get √248 = (√4)(√62) = 2√62 ≈ 15.748  Print the puzzles or type the factors on this excel file: 10 Factors 2014-09-29

A Logical Approach to FIND THE FACTORS: Find the column or row with two clues and find their common factor. Write the corresponding factors in the factor column (1st column) and factor row (top row).  Because this is a level three puzzle, you have now written a factor at the top of the factor column. Continue to work from the top of the factor column to the bottom, finding factors and filling in the factor column and the factor row one cell at a time as you go. 