Prime number

107 and Level 6

/ ivasallay / Leave a comment
  • 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

 

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

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

89 and Level 1

/ ivasallay / Leave a comment
  • 89 is a prime number.
  • Prime factorization: 89 is prime.
  • The exponent of prime number 89 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 89 has exactly 2 factors.
  • Factors of 89: 1, 89
  • Factor pairs: 89 = 1 x 89
  • 89 has no square factors that allow its square root to be simplified. √89 ≈ 9.43398

How do we know that 89 is a prime number? If 89 were not a prime number, then it would be divisible by at least one prime number less than or equal to √89 ≈ 9.4. Since 89 cannot be divided evenly by 2, 3, 5, or 7, we know that 89 is a prime number.

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

2014-15 Level 1

 

This week’s puzzles and last week’s solutions: 10 Factors 2014-04-14

2014-15 Level 1 Factors

83 and Level 1

/ ivasallay / Leave a comment

2014-14 Level 1

This week’s puzzles and last week’s solutions: 12 Factors 2014-04-07

  • 83 is a prime number.
  • Prime factorization: 83 is prime.
  • The exponent of prime number 83 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 83 has exactly 2 factors.
  • Factors of 83: 1, 83
  • Factor pairs: 83 = 1 x 83
  • 83 has no square factors that allow its square root to be simplified. √83 ≈ 9.11043

How do we know that 83 is a prime number? If 83 were not a prime number, then it would be divisible by at least one prime number less than or equal to √83 ≈ 9.1. Since 83 cannot be divided evenly by 2, 3, 5, or 7, we know that 83 is a prime number.

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

 2014-14 Level 1 Factors

79 and Level 3

/ ivasallay / Leave a comment

2014-13 Level 3

This week’s puzzles and last week’s solutions: 10 Factors 2014-03-31

  • 79 is a prime number.
  • Prime factorization: 79 is prime.
  • The exponent of prime number 79 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 79 has exactly 2 factors.
  • Factors of 79: 1, 79
  • Factor pairs: 79 = 1 x 79
  • 79 has no square factors that allow its square root to be simplified. √79 ≈ 8.8881944

How do we know that 79 is a prime number? If 79 were not a prime number, then it would be divisible by at least one prime number less than or equal to √79 ≈ 8.8. Since 79 cannot be divided evenly by 2, 3, 5, or 7, we know that 79 is a prime number.

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

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:

2014-13 Level 3 Factors

73 and Once

/ ivasallay / Leave a comment

In Hungarian, “Multiplication Table” and “Times Table” are the same expression as “Once Upon a Time”. I very much enjoyed learning that when I went to the school of fairies today where even butterflies can learn to multiply. The author translates a sweet poem from Hungarian into English. I hope you will read the poem and remember its encouraging words whenever you try to solve one of my multiplication table puzzles or any other task that challenges you in life.

  • 73 is a prime number.
  • Prime factorization: 73 is prime.
  • The exponent of prime number 73 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 73 has exactly 2 factors.
  • Factors of 73: 1, 73
  • Factor pairs: 73 = 1 x 73
  • 73 has no square factors that allow its square root to be simplified. √73 ≈ 8.5440037

How do we know that 73 is a prime number? If 73 were not a prime number, then it would be divisible by at least one prime number less than or equal to √73 ≈ 8.5. Since 73 cannot be divided evenly by 2, 3, 5, or 7, we know that 73 is a prime number.

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

73 is included in this list of prime numbers:

 

71 and Level 3

/ ivasallay / Leave a comment

 

2014-12 Level 3

This week’s puzzles for you to solve

Here’s a little about the number 71:

  • 71 is a prime number.
  • Prime factorization: 71 is prime.
  • The exponent of prime number 71 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 71 has exactly 2 factors.
  • Factors of 71: 1, 71
  • Factor pairs: 71 = 1 x 71
  • 71 has no square factors that allow its square root to be simplified. √71 ≈ 8.4261

How do we know that 71 is a prime number? If 71 were not a prime number, then it would be divisible by at least one prime number less than or equal to √71 ≈ 8.4. Since 71 cannot be divided evenly by 2, 3, 5, or 7, we know that 71 is a prime number.

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

A Logical Approach to the Solution of the puzzle: 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 as you go:

2014-12 Level 3 Factors

67 and How to get more blog followers

/ ivasallay / 3 Comments

 

Shortly after I started blogging, Steve Morris found me and became a leader in my cheering section. Even after the number of HIS followers grew exponentially, he still finds some time to show me support.

Here he writes an entertaining and encouraging post titled How To Get More Blog Followers that I think all bloggers should read. It has a mathematical element to it and could help you increase the number of people who read your blog even if your own mother isn’t one of them.

Now here’s a little about the number 67:

  • 67 is a prime number.
  • Prime factorization: 67 is prime.
  • The exponent of prime number 67 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 67 has exactly 2 factors.
  • Factors of 67: 1, 67
  • Factor pairs: 67 = 1 x 67
  • 67 has no square factors that allow its square root to be simplified. √67 ≈ 8.18535

How do we know that 67 is a prime number? If 67 were not a prime number, then it would be divisible by at least one prime number less than or equal to √67 ≈ 8.2. Since 67 cannot be divided evenly by 2, 3, 5, or 7, we know that 67 is a prime number.

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

61 and Opportunity to Catch Up

/ ivasallay / 2 Comments
  • 61 is a prime number.
  • Prime factorization: 61 is prime.
  • The exponent of prime number 61 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 61 has exactly 2 factors.
  • Factors of 61: 1, 61
  • Factor pairs: 61 = 1 x 61
  • 61 has no square factors that allow its square root to be simplified. √61 ≈ 7.8102

How do we know that 61 is a prime number? If 61 were not a prime number, then it would be divisible by at least one prime number less than or equal to √61 ≈ 7.8. Since 61 cannot be divided evenly by 2, 3, 5, or 7, we know that 61 is a prime number.

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

2014-06 Level 4

Wedding Bells are Going to Chime

My daughter is getting married in early March, and family will be coming in from out of town. I also need to study for a test at work. There is so much that needs to get done that hasn’t been getting done. I’m taking a month-long break from daily blogging and a few other things so I can catch up on the things that just can’t wait. 

Over the last several weeks there has been several new people who have found this blog and have done some of the puzzles. Some of them have clicked on the older excel files to work on puzzles. All that clicking was probably inconvenient, but several people have still clicked anyway. Thank you for your interest and persistence. I want to make it easier to catch up on all those old puzzles.

To make it easier to access the older puzzles, I’ve put all previously published FIND THE FACTORS 1-10 and 1-12 puzzles in one excel file, All Previously Published Puzzles. The formatting isn’t printer friendly, but if you enable editing, you can type the factors directly onto the excel file. The answers are also in the file for easy comparison with your work. (Hopefully, I didn’t mess up any of the clues while I hurriedly created this large file. Please, tell me if you find any errors.)

2014-06 Level 4 Answer

While I catch up on all the things I need to do, I hope you will catch up a few things as well.