125 is a composite number. 125 = 1 x 125 or 5 x 25. Factors of 125: 1, 5, 25, 125. Prime factorization: 125 = 5 x 5 x 5, which can also be written 125 = 5³.
125 is never a clue in the FIND THE FACTORS puzzles.
Placing the last few factors on this Level 4 puzzle may be a bit trickier than usual. As always, use logic, not guessing and checking, to find its one and only solution. Good luck!
Excel file of this week’s puzzles and last week’s factors: 12 Factors 2014-05-19
119 is a composite number. 119 = 1 x 119 or 7 x 17. Factors of 119: 1, 7, 17, 119. Prime factorization: 119 = 7 x 17.
119 is never a clue in the FIND THE FACTORS puzzles.
119 is the sum of consecutive prime numbers two ways. Each way begins with one of its prime factors!
7 + 11 + 13 + 17 + 19 + 23 + 29 = 119 (That’s 7 consecutive primes!)
17 + 19 + 23 + 29 + 31 = 119
Excel file of this week’s puzzles and last week’s factors: 10 Factors 2014-05-12
Some people get the factors of 54 and 56 mixed up. If you get them mixed up on this particular puzzle, you could still think you solved the puzzle correctly even if you haven’t. Here’s a couple of tricks that might prevent the mix-ups:
One of my favorite multiplication rhymes is “Five, Six, Seven, Eight, Fifty-Six is Seven Times Eight,” so 56 = 7 x 8.
Notice that 5 + 4 = 9. The sum of the digits of any multiple of 9 will always be 9 or another multiple of 9, so 54 = 9 x 6. On the other hand, 5 + 6 = 11, so 56 cannot have 9 as one of its factors.
Excel file of six puzzles and the previous week’s solutions: 12 Factors 2014-05-05
112 is a composite number. 112 = 1 x 112, 2 x 56, 4 x 28, 7 x 16, or 8 x 14. Factors of 112: 1, 2, 4, 7, 8, 14, 16, 28, 56, 112. Prime factorization: 112 = 2 x 2 x 2 x 2 x 7, which can also be written 112 = 2⁴ x 7.
112 is never a clue in the FIND THE FACTORS puzzles.
24 is divisible by the sum of its digits and by the product of its digits. So too is 112. Is there a four-digit number with this property? A five-digit one? In general, for each count of digits, is there a number double divisible in this way? pic.twitter.com/PkruSSvx9K
— James Tanton (@jamestanton) March 21, 2021
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.
This week’s puzzles and last week’s solutions: 10 Factors 2014-04-28
99 is a composite number. 99 = 1 x 99, 3 x 33, or 9 x 11. Factors of 99: 1, 3, 9, 11, 33, 99. Prime factorization: 99 = 3 x 3 x 11, which can also be written 99 = 3² x 11.
Sometimes 99 is a clue in the FIND THE FACTORS 1 – 12 puzzles. Even though it has other factors, we use only 9 x 11 in the puzzles.
This week’s puzzles and last week’s solutions: 12 Factors 2014-04-21
93 is a composite number. 93 = 1 x 93 or 3 x 31. The factors of 93: 1, 3, 31, 93. Prime factorization: 93 = 3 x 31.
93 is never a clue in the FIND THE FACTORS puzzles.
This week’s puzzles and last week’s solutions: 10 Factors 2014-04-14
86 is a composite number. 86 = 1 x 86 or 2 x 43. Factors of 86: 1, 2, 43, 86. Prime factorization: 86 = 2 x 43.
86 is never a clue in the FIND THE FACTORS puzzles.
This week’s puzzles and last week’s solutions: 12 Factors 2014-04-07
WordPress measures how many posts are written about certain topics each month and then they publish their findings. The results for March were published in the march-hot-list/. Cat lovers were informed, “your beloved felines yet again got trounced by their canine frenemies. Dogs: 10,589; cats: 6,401. Is that a big, defiant “meow” we hear? Maybe you’ll do better in April.”
I have two sisters who truly love their cats. Although I personally prefer neither pet over the other, I hate to see cats so clearly in the “underdog” role. Today’s puzzle looks a teeny tiny bit like the head of a cat, so I’m tagging it with the word “cats.” Of course, this post alone will not be enough to make much of a difference in April’s statistics.
This week’s puzzles and last week’s solutions: 10 Factors 2014-03-31
80 is a composite number. 80 = 1 x 80, 2 x 40, 4 x 20, 5 x 16, and 8 x 10. Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80. Prime factorization: 80 = 2 x 2 x 2 x 2 x 5 which can also be written 80 = 2⁴ x 5.
Sometimes 80 is a clue in the FIND THE FACTORS puzzles. Even though it has other factors, the only multiplication fact we use is 8 x 10 = 80.
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.
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.
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.)
While I catch up on all the things I need to do, I hope you will catch up a few things as well.