# 76 and Level 1

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

76 is a composite number. 76 = 1 x 76, 2 x 38, or 4 x 19. Factors of 76: 1, 2, 4, 19, 38, 76, Prime factorization: 76 = 2 x 2 x 19, which can also be written 2² x 19.

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

# 75 and Level 6

This week’s puzzles for you to solve

75 is a composite number. 75 = 1 x 75, 3 x 25, or 5 x 15. Factors of 75: 1, 3, 5, 15, 25, 75. Prime factorization: 75 = 3 x 5 x 5, which can also be written 75 = 3 x 5².

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

# 74 and Level 5

This week’s puzzles for you to solve

74 is a composite number. 74 = 1 x 74 or 2 x 37. Factors of 74: 1, 2, 37, 74. Prime factorization: 74 = 2 x 37.

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

# 73 and Once

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.

# 72 and Level 4

This week’s puzzles for you to solve

Here are some facts about the number 72:

72 is a composite number. 72 = 1 x 72, 2 x 36, 3 x 24, 4 x 18, 6 x 12, or 8 x 9. Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. Prime factorization: 72 = 2 x 2 x 2 x 3 x 3, which can also be written 2³ x 3²

Sometimes 72 is a clue in the Find the Factors puzzles. Even though it has many other factors, we use only 8 x 9 for the FIND THE FACTORS 1-10 puzzles and 8 x 9 or 6 x 12 for the FIND THE FACTORS 1-12 puzzles.

# 71 and 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:

# 70 and Level 2

This week’s puzzles for you to solve

70 is a composite number. 70 = 1 x 70, 2 x 35, 5 x 14, and 7 x 10. Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70. Prime factorization: 70 = 2 x 5 x 7.

Sometimes 70 is a clue in the FIND THE FACTORS 1 – 12 puzzles. Even though it has other factors, we only use 70 = 7 x 10 in the puzzles.

Here are the factors for today’s puzzle:

# 69 and Six!

The number 6 appears twice as a clue in today’s puzzle. It shouldn’t be difficult to figure out why I put “Six!” in this post’s title.

This week’s puzzles for you to solve

69 is a composite number. 69 = 1 x 69 or 3 x 23. Factors of 69: 1, 3, 23, 69. Prime factorization: 69 = 3 x 23.

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

Here are the factors for today’s puzzle:

# 68 and Happy Saint Patrick’s Day!

68 is a composite number. 68 = 1 x 68, 2 x 34, or 4 x 17. Factors of 68: 1, 2, 4, 17, 34, 68. Prime factorization: 68 = 2 x 2 x 17, which can also be written 2² x 17.

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

All Previously Published Puzzles

I survived my daughter’s wedding. The last of our out-of-state visitors will be going home tomorrow. AND my computer that broke and spent a week in the shop is working again. I will publish six new puzzles next Monday.

# 67 and How to get more blog followers

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.