• 288 is a composite number.
• Prime factorization: 288 = 2 x 2 x 2 x 2 x 2 x 3 x 3, which can be written 288 = (2^5) x (3^2)
• The exponents in the prime factorization are 5 and 2. Adding one to each and multiplying we get (5 + 1)(2 + 1) = 6 x 3  = 18. Therefore 288 has exactly 18 factors.
• Factors of 288: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
• Factor pairs: 288 = 1 x 288, 2 x 144, 3 x 96, 4 x 72, 6 x 48, 8 x 36, 9 x 32, 12 x 24, or 16 x 18
• Taking the factor pair with the largest square number factor, we get √288 = (√2)(√144) = 12√2 ≈ 16.971

Print the puzzles or type the factors on this excel file: 12 Factors 2014-11-03

• 287 is a composite number.
• Prime factorization: 287 = 7 x 41
• The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 x 2 = 4. Therefore 287 has 4 factors.
• Factors of 287: 1, 7, 41, 287
• Factor pairs: 287 = 1 x 287 or 7 x 41
• 287 has no square factors that allow its square root to be simplified. √287 ≈ 16.941.

Here’s today’s puzzle:

Print the puzzles or type the factors on this excel file: 12 Factors 2014-11-03

• 286 is a composite number.
• Prime factorization: 286 = 2 x 11 x 13
• The exponents in the prime factorization are 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 x 2 x 2 = 8. Therefore 286 has 8 factors.
• Factors of 286: 1, 2, 11, 13, 22, 26, 143, 286
• Factor pairs: 1 x 286, 2 x 143, 11 x  26, or 13 x 22
• 286 has no square factors that allow its square root to be simplified. √286 ≈ 16.912

Print the puzzles or type the factors on this excel file: 12 Factors 2014-11-03

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.

• 285 is a composite number.
• Prime factorization: 285 = 3 x 5 x 19
• The exponents in the prime factorization are 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 x 2 x 2 = 8. Therefore 285 has 8 factors.
• Factors of 285: 1, 3, 5, 15, 19, 57, 95, 285
• Factor pairs: 1 x 185, 3 x 95, 5 x 57, or 15 x 19
• 285 has no square factors that allow its square root to be simplified. √285 ≈ 16.882

Print the puzzles or type the factors on this excel file: 12 Factors 2014-11-03

• 284 is a composite number.
• Prime factorization: 284 = 2 x 2 x 71, which can be written 284 = 2² x 71
• The exponents in the prime factorization are 2 and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1) = 3 x 2  = 6. Therefore 284 has exactly 6 factors.
• Factors of 284: 1, 2, 4, 71, 142, 284
• Factor pairs: 284 = 1 x 284, 2 x 142, or 4 x 71
• Taking the factor pair with the largest square number factor, we get √284 = (√4)(√71) = 2√71 ≈ 16.852

Print the puzzles or type the factors on this excel file: 12 Factors 2014-11-03