• 255 is a composite number.
• Prime factorization: 255 = 3 x 5 x 17
• 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 255 has 8 factors.
• Factors of 255: 1, 3, 5, 15, 17, 51, 85, 255
• Factor pairs: 255 = 1 x 255, 3 x 85, 5 x 51, or 15 x 17
• 255 has no square factors that allow its square root to be simplified. √255 ≈ 15.969

Here’s a factoring puzzle for you to solve:

Print the puzzles or type the factors on this excel file: 12 Factors 2014-10-06

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.

• 254 is a composite number.
• Prime factorization: 254 = 2 x 127
• 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 254 has 4 factors.
• Factors of 254: 1, 2, 127, 254
• Factor pairs: 254 = 1 x 254 or 2 x 127
• 254 has no square factors that allow its square root to be simplified. √254 ≈ 15.937

Print the puzzles or type the factors on this excel file: 12 Factors 2014-10-06

• 253 is a composite number.
• Prime factorization: 253 = 11 x 23
• 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 253 has 4 factors.
• Factors of 253: 1, 11, 23, 253
• Factor pairs: 253 = 1 x 253 or 11 x 23
• 253 has no square factors that allow its square root to be simplified. √253 ≈ 15.906

Print the puzzles or type the factors on this excel file: 12 Factors 2014-10-06

• 250 is a composite number.
• Prime factorization: 250 = 2 x 5 x 5 x 5, which can be written 250 = 2 x (5^3)
• The exponents in the prime factorization are 1 and 3. Adding one to each and multiplying we get (1 + 1)(3 + 1) = 2 x 4 = 8. Therefore 250 has 8 factors.
• Factors of 250: 1, 2, 5, 10, 25, 50, 125, 250
• Factor pairs: 250 = 1 x 250, 2 x 125, 5 x 50, or 10 x 25
• Taking the factor pair with the largest square number factor, we get √250 = (√10)(√25) = 5√10 ≈ 15.811

Print the puzzles or type the factors on this excel file: 10 Factors 2014-09-29

• 249 is a composite number.
• Prime factorization: 249 = 3 x 83
• 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 249 has 4 factors.
• Factors of 249: 1, 3, 83, 249
• Factor pairs: 249 = 1 x 249 or 3 x 83
• 249 has no square factors so its square root cannot be simplified. √249 ≈ 15.7797

Print the puzzles or type the factors on this excel file: 10 Factors 2014-09-29

• 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.

• 247 is a composite number.
• Prime factorization: 247 = 13 x 19
• 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 247 has 4 factors.
• Factors of 247: 1, 13, 19, 247
• Factor pairs: 247 = 1 x 247 or 13 x 19
• 247 has no square factors so its square root cannot be simplified. √247 ≈ 15.716

Print the puzzles or type the factors on this excel file: 10 Factors 2014-09-29

• 244 is a composite number.
• Prime factorization: 244 = 2 x 2 x 61, which can be written 244 = (2^2) x 61
• 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 244 has 6 factors.
• Factors of 244: 1, 2, 4, 61, 122, 244
• Factor pairs: 244 = 1 x 244, 2 x 122, 4 x 61
• Taking the factor pair with the largest square number factor, we get √244 = (√4)(√61) = 2√61 ≈ 15.6205

Print the puzzles or type the factors on this excel file: 12 Factors 2014-09-22