Level 2 Puzzle

254 and Level 2

/ ivasallay / Leave a comment

  • 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

2014-40 Level 2

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

2014-40 Level 2 Factors

247 and Level 2

/ ivasallay / Leave a comment

  • 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

2014-39 Level 2

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

2014-39 Level 2 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

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

227 and Level 2

/ ivasallay / Leave a comment

  • 227 is a prime number.
  • Prime factorization: 227 is prime.
  • The exponent of prime number 227 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 227 has exactly 2 factors.
  • Factors of 227: 1, 227
  • Factor pairs: 227 = 1 x 227
  • 227 has no square factors so its square root cannot be simplified. √227 ≈ 15.067

How do we know that 227 is a prime number? If 227 were not a prime number, then it would be divisible by at least one prime number less than or equal to √227 ≈ 15.067. Since 227 cannot be divided evenly by 2, 3, 5, 7, 11, or 13, we know that 227 is a prime number.

2014-36 Level 2

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

2014-36 Level 2 Factors

220 and Level 2

/ ivasallay / Leave a comment

  • 220 is a composite number.
  • Prime factorization: 220 = 2 x 2 x 5 x 11, which can be written (2^2) x 5 x 11
  • 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 220 has 12 factors.
  • Factors of 220: 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220
  • Factor pairs: 220 = 1 x 220, 2 x 110, 4 x 55, 5 x 44, 10 x 22,  or 11 x 20
  • Taking the factor pair with the largest square number factor, we get √220 = (√4)( √55) = 2√55 ≈ 14.832

2014-35 Level 2

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

2014-35 Level 2 Factors

214 and Level 2

/ ivasallay / Leave a comment

  • 214 is a composite number.
  • Prime factorization: 214 = 2 x 107
  • 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 214 has 4 factors.
  • Factors of 214: 1, 2, 107, 214
  • Factor pairs: 214 = 1 x 214 or 2 x 107
  • Since 214 has no square factors, the square root of 214 cannot be simplified. √214 ≈ 14.629

2014-34 Level 2

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

2014-34 Level 2 Factors

208 and Level 2

/ ivasallay / Leave a comment

  • 208 is a composite number.
  • Prime factorization: 208 = 2 x 2 x 2 x 2 x 13, which can be written 208 = 2⁴ x 13
  • The exponents in the prime factorization are 4 and 1. Adding one to each and multiplying we get (4 + 1)(1 + 1) = 5 x 2 = 10. Therefore 208 has exactly 10 factors.
  • Factors of 208: 1, 2, 4, 8, 13, 16, 26, 52, 104, 208
  • Factor pairs: 208 = 1 x 208, 2 x 104, 4 x 52, 8 x 26, or 13 x 16
  • Taking the factor pair with the largest square number factor, we get √208 = (√16)(√13) = 4√13 ≈ 14.422205

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 2014-33 Level 2

Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-08-18

2014-33 Level 2 Factors

202 and Level 2

/ ivasallay / Leave a comment

  • 202 is a composite number.
  • Prime factorization: 202 = 2 x 101
  • 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 202 has exactly 4 factors.
  • Factors of 202: 1, 2, 101, 202
  • Factor pairs: 202 = 1 x 202 or 2 x 101
  • 202 has no square factors that allow its square root to be simplified. √202 ≈ 14.2126704

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2014-32 Level 2

Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-08-11

2014-32 Level 2 Factors

193 and Level 2

/ ivasallay / Leave a comment
  • 193 is a prime number.
  • Prime factorization: 193 is prime.
  • The exponent of prime number 193 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 193 has exactly 2 factors.
  • Factors of 193: 1, 193
  • Factor pairs: 193 = 1 x 193
  • 193 has no square factors that allow its square root to be simplified. √193 ≈ 13.89244

How do we know that 193 is a prime number? If 193 were not a prime number, then it would be divisible by at least one prime number less than or equal to √193 ≈ 13.9. Since 193 cannot be divided evenly by 2, 3, 5, 7, 11, or 13, we know that 193 is a prime number.

2014-31 Level 2

Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-08-04

2014-31 Level 2 Factors