• 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.

• 234 is a composite number.
• Prime factorization: 234 = 2 x 3 x 3 x 13, which can be written 2 x (3^2) x 13
• The exponents in the prime factorization are 1, 2 and 1. Adding one to each and multiplying we get (1 + 1)(2 + 1)(1 + 1) = 2 x 3 x 2 = 12. Therefore 234 has 12 factors.
• Factors of 234: 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234
• Factor pairs: 234 = 1 x 234, 2 x 117, 3 x 78, 6 x 39, 9 x 26, or 13 x 18
• Taking the factor pair with the largest square number factor, we get √234 = (√9)( √26) = 3√26 ≈ 15.297

Print the puzzles or type the factors on this excel file: 10 Factors 2014-09-15

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.

• 228 is a composite number.
• Prime factorization: 228 = 2 x 2 x 3 x 19, which can be written 228 = (2^2) x 3 x 19.
• The exponents in the prime factorization are 2, 1, and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1)(1 + 1) = 3 x 2 x 2 = 12. Therefore 228 has 12 factors.
• Factors of 228: 1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 228
• Factor pairs: 228 = 1 x 228, 2 x 114, 3 x 76, 4 x 57, 6 x 38, or 12 x 19
• Taking the factor pair with the largest square number factor, we get √228 = (√4)( √57) = 2√57 ≈ 15.0997

Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-09-08

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.

• 221 is a composite number.
• Prime factorization: 221 = 13 x 17
• 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 221 has 4 factors.
• Factors of 221: 1, 13, 17, 221
• Factor pairs: 221 = 1 x 221 or 13 x 17
• 221 has no square factors so its square root cannot be simplified. √221 ≈ 14.866

Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-09-01

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.

• 215 is a composite number.
• Prime factorization: 215 = 5 x 43
• The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1) x (1 + 1) = 2 x 2 = 4. Therefore 215 has 4 factors.
• Factors of 215: 1, 5, 43, 215
• Factor pairs: 215 = 1 x 215 or 5 x 43
• Since 215 has no square factors, the square root of 215 cannot be simplified. √215 ≈ 14.663

Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-08-25

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.