Multiplication table

243 and Level 5

/ ivasallay / 1 Comment

  • 243 is a composite number.
  • Prime factorization: 243 = 3 x 3 x 3 x 3 x 3, which can be written 243 = (3^5)
  • The exponent in the prime factorization is 5. Adding one we get (5 + 1) = 6. Therefore 243 has 6 factors.
  • Factors of 243: 1, 3, 9, 27, 81, 243
  • Factor pairs: 243 = 1 x 243, 3 x 81, or 9 x 27
  • Taking the factor pair with the largest square number factor, we get √243 = (√3)(√81) = 9√3 ≈ 15.588

Happy birthday, Sue

This puzzle is for my sister, who is great at completing these Level 5 puzzles. Here is a black and white version for those who may prefer it:

2014-38 Level 5

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

2014-38 Level 5 Logic

242 and Level 4

/ ivasallay / Leave a comment

  • 242 is a composite number.
  • Prime factorization: 242 = 2 x 11 x 11, which can be written 2 x (11^2)
  • The exponents in the prime factorization are 1 and 2. Adding one to each and multiplying we get (1 + 1)(2 + 1) = 2 x 3 = 6. Therefore 242 has 6 factors.
  • Factors of 242: 1, 2, 11, 22, 121, 242
  • Factor pairs: 242 = 1 x 242, 2 x 121, or 11 x 22
  • Taking the factor pair with the largest square number factor, we get √242 = (√2)(√121) = 11√2 ≈ 15.556

2014-38 Level 4

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

2014-38 Level 4 Logic

241 and Level 3

/ ivasallay / Leave a comment

  • 241 is a prime number.
  • Prime factorization: 241 is prime.
  • The exponent of prime number 241 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 241 has exactly 2 factors.
  • Factors of 241: 1, 241
  • Factor pairs: 241 = 1 x 241
  • 241 has no square factors so its square root cannot be simplified. √241 ≈ 15.524

How do we know that 241 is a prime number? If 241 were not a prime number, then it would be divisible by at least one prime number less than or equal to √241 ≈ 15.524. Since 241 cannot be divided evenly by 2, 3, 5, 7, 11, or 13, we know that 241 is a prime number.

2014-38 Level 3

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

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.

2014-38 Level 3 Factors

239 and Level 2

/ ivasallay / Leave a comment

  • 239 is a prime number.
  • Prime factorization: 239 is prime.
  • The exponent of prime number 239 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 239 has exactly 2 factors.
  • Factors of 239: 1, 239
  • Factor pairs: 239 = 1 x 239
  • 239 has no square factors so its square root cannot be simplified. √239 ≈ 15.4596

How do we know that 239 is a prime number? If 239 were not a prime number, then it would be divisible by at least one prime number less than or equal to √239 ≈ 15.4596. Since 239 cannot be divided evenly by 2, 3, 5, 7, 11, or 13, we know that 239 is a prime number.

2014-38 Level 2

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

2014-38 Level 2 Factors

238 and Level 1

/ ivasallay / Leave a comment

  • 238 is a composite number.
  • Prime factorization: 238 = 2 x 7 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 238 has 8 factors.
  • Factors of 238: 1, 2, 7, 14, 17, 34, 119, 238
  • Factor pairs: 238 = 1 x 238, 2 x 119, 7 x 34, or 14 x 17
  • Since 238 has no square number factors, its square root cannot be simplified. √238 ≈ 15.427

2014-38 Level 1

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

2014-38 Level 1 Factors

237 and Level 6

/ ivasallay / Leave a comment

  • 237 is a composite number.
  • Prime factorization: 237 = 3 x 79
  • 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 237 has 4 factors.
  • Factors of 237: 1, 3, 79, 237
  • Factor pairs: 237 = 1 x 237 or 3 x 79
  • Since 237 has no square number factors, its square root cannot be simplified. √237 ≈ 15.395

2014-37 Level 6

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

2014-37 Level 6 Logic

236 and Level 5

/ ivasallay / Leave a comment

  • 236 is a composite number.
  • Prime factorization: 236 = 2 x 2 x 59, which can be written (2^2) x 59
  • 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 236 has 6 factors.
  • Factors of 236: 1, 2, 4, 59, 118, 236
  • Factor pairs: 236 = 1 x 236, 2 x 118, or 4 x 59
  • Taking the factor pair with the largest square number factor, we get √236 = (√4)( √59) = 2√59 ≈ 15.362

2014-37 Level 5

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

2014-37 Level 5 Logic

235 and Level 4

/ ivasallay / Leave a comment

  • 235 is a composite number.
  • Prime factorization: 235 = 5 x 47
  • 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 235 has 4 factors.
  • Factors of 235: 1, 5, 47, 235
  • Factor pairs: 235 = 1 x 235 or 5 x 47
  • Since 235 has no square number factors, its square root cannot be simplified. √235 ≈ 15.3297

2014-37 Level 4

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

2014-37 Level 4 Logic

234 and Level 3

/ ivasallay / Leave a comment

  • 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

2014-37 Level 3

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.

2014-37 Level 3 Factors

233 and Level 2

/ ivasallay / Leave a comment

  • 233 is a prime number.
  • Prime factorization: 233 is prime.
  • The exponent of prime number 233 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 233 has exactly 2 factors.
  • Factors of 233: 1, 233
  • Factor pairs: 233 = 1 x 233
  • 233 has no square factors so its square root cannot be simplified. √233 ≈ 15.264

How do we know that 233 is a prime number? If 233 were not a prime number, then it would be divisible by at least one prime number less than or equal to √233 ≈ 15.264. Since 233 cannot be divided evenly by 2, 3, 5, 7, 11, or 13, we know that 233 is a prime number.

2014-37 Level 2

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

2014-37 Level 2 Factors