divisors

110 and Level 3

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110 is a composite number. 110 = 1 x 110, 2 x 55, 5 x 22, or 10 x 11. Factors of 110: 1, 2, 5, 10, 11, 22, 55, 110. Prime factorization: 110 = 2 x 5 x 11.

When 110 is a clue in the FIND THE FACTORS 1 – 12 puzzles, use 10 and 11 as the factors.

2014-18 Level 3

Excel file of puzzles and the previous week’s solutions: 12 Factors 2014-05-05

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:

2014-18 Level 3 Factors

109 and Level 2

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  • 109 is a prime number.
  • Prime factorization: 109 is prime.
  • The exponent of prime number 109 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 109 has exactly 2 factors.
  • Factors of 109: 1, 109
  • Factor pairs: 109 = 1 x 109
  • 109 has no square factors that allow its square root to be simplified. √109 ≈ 10.4403

How do we know that 109 is a prime number? If 109 were not a prime number, then it would be divisible by at least one prime number less than or equal to √109 ≈ 10.4 Since 109 cannot be divided evenly by 2, 3, 5, or 7, we know that 109 is a prime number.

109 is never a clue in the FIND THE FACTORS puzzles.

2014-18 Level 2

This week’s puzzles and last weeks solutions: 12 Factors 2014-05-05

2014-18 Level 2 Factors

108 and Level 1

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108 is a composite number. 108 = 1 x 108, 2 x 54, 3 x 36, 4 x 27, 6 x 18, or 9 x 12. Factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108. Prime factorization: 108 = 2 x 2 x 3 x 3 x 3, which can also be written 108 = 2² x 3³

When 108 is a clue in the FIND THE FACTORS 1 – 12 puzzles, use 9 and 12 as the factors.

2014-18 Level 1

This week’s puzzles and last weeks solutions: 12 Factors 2014-05-05

2014-18 Level 1 Factors

 

107 and Level 6

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  • 107 is a prime number.
  • Prime factorization: 107 is prime.
  • The exponent of prime number 107 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 107 has exactly 2 factors.
  • Factors of 107: 1, 107
  • Factor pairs: 107 = 1 x 107
  • 107 has no square factors that allow its square root to be simplified. √107 ≈ 10.34408

How do we know that 107 is a prime number? If 107 were not a prime number, then it would be divisible by at least one prime number less than or equal to √107 ≈ 10.3 Since 107 cannot be divided evenly by 2, 3, 5, or 7, we know that 107 is a prime number.

107 is never a clue in the FIND THE FACTORS puzzles.

2014--17 Level 6

This week’s puzzles and last week’s solutions: 10 Factors 2014-04-28

2014-17 Level 6 Logic

 

106 and Level 5

/ ivasallay / 2 Comments

106 is a composite number. 106 = 1 x 106 or 2 x 53. Factors of 106: 1, 2, 53, 106. Prime factorization: 106 = 2 x 53.

106 is never a clue in the FIND THE FACTORS  puzzles.

2014-17 Level 5

This week’s puzzles and last week’s solutions: 10 Factors 2014-04-28

2014-17 Level 5 Logic

105 and Level 4

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105 is a composite number. 105 = 1 x 105, 3 x 35, 5 x 21, 7 x 15. Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105. Prime factorization: 105 = 3 x 5 x 7.

105 is never a clue in the FIND THE FACTORS puzzles.

2014-17 Level 4

This week’s puzzles and last week’s solutions: 10 Factors 2014-04-28

2014-17 Level 4 Logic

104 and Level 3

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104 is a composite number. 104 = 1 x 104, 2 x 52, 4 x 26, or 8 x 13. Factors of 104: 1, 2, 4, 8, 13, 26, 52, 104. Prime factorization: 104 = 2 x 2 x 2 x 13, which can also be written 2³ x 13.

104 is never a clue in the FIND THE FACTORS puzzles.

2014-17 Level 3

The week’s puzzles and the previous week’s solutions: 10 Factors 2014-04-28

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 and factor 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 table one row at a time as you go:

2014-17 Level 3 factors

103 and Level 2

/ ivasallay / 2 Comments
  • 103 is a prime number.
  • Prime factorization: 103 is prime.
  • The exponent of prime number 103 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 103 has exactly 2 factors.
  • Factors of 103: 1, 103
  • Factor pairs: 103 = 1 x 103
  • 103 has no square factors that allow its square root to be simplified. √103 ≈ 10.14889

How do we know that 103 is a prime number? If 103 were not a prime number, then it would be divisible by at least one prime number less than or equal to √103 ≈ 10.1 Since 103 cannot be divided evenly by 2, 3, 5, or 7, we know that 103 is a prime number.

103 is never a clue in the FIND THE FACTORS puzzles.

2014-17 Level 2

This week’s puzzles and last week’s factors: 10 Factors 2014-04-28

2014-17 Level 2 factors

102 and Level 1

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102 is a composite number. 102 = 1 x 102, 2 x 51, 3 x 34, or 6 x 17. Factors of 102: 1, 2, 3, 6, 17, 34, 51, 102. Prime factorization: 102 = 2 x 3 x 17.

102 is never a clue in the FIND THE FACTORS puzzles.

2014-17 Level 1

This week’s puzzles and last week’s solutions: 10 Factors 2014-04-28

2014-17 Level 1 factors

101 and Level 6

/ ivasallay / 3 Comments
  • 101 is a prime number.
  • Prime factorization: 101 is prime.
  • The exponent of prime number 101 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 101 has exactly 2 factors.
  • Factors of 101: 1, 101
  • Factor pairs: 101 = 1 x 101
  • 101 has no square factors that allow its square root to be simplified. √101 ≈ 10.0498756

How do we know that 101 is a prime number? If 101 were not a prime number, then it would be divisible by at least one prime number less than or equal to √101 ≈ 10. Since 101 cannot be divided evenly by 2, 3, 5, or 7, we know that 101 is a prime number.

101 is never a clue in the FIND THE FACTORS puzzles.

2014-16 Level 6

This week’s puzzles and last week’s solutions: 12 Factors 2014-04-21

2014-16 Level 6 Logic