This week’s puzzles and last week’s solutions: 10 Factors 2014-03-31
77 is a composite number. 77 = 1 x 77 or 7 x 11. Factors of 77: 1, 7, 11, 77. Prime factorization: 77 = 7 x 11.
Sometimes 77 is a clue in the FIND THE FACTORS 1 – 12 puzzles. Even though it has other factors, the puzzle only uses 7 x 11 = 77.
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.
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.
75 is in this wonderful pattern. Can you tell what the pattern is?
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.
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.
This week’s puzzles for you to solve
Here’s a little about the number 71:
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:
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:
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 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.
66 is a composite number. 66 = 1 x 66, 2 x 33, 3 x 22, or 6 x 11. Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66. Prime factorization: 66 = 2 x 3 x 11.
Sometimes 66 is a clue in the FIND THE FACTORS 1 – 12 puzzles. Even though it has other factors, the puzzle only uses 6 x 11 = 66.
I like this fractal animation very much! It really goes on forever!