1227 and Level 4

I’m confident you know a common factor of 42 and 60 for which ALL the factors involved are numbers from 1 to 10. That’s all you need to know to start this puzzle. Go ahead, give it a try!

Print the puzzles or type the solution in this excel file: 10-factors-1221-1231

Here is some information about the number 1227:

  • 1227 is a composite number.
  • Prime factorization: 1227 = 3 × 409
  • The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 1227 has exactly 4 factors.
  • Factors of 1227: 1, 3, 409, 1227
  • Factor pairs: 1227 = 1 × 1227 or 3 × 409
  • 1227 has no square factors that allow its square root to be simplified. √1227 ≈ 35.02856

1227 is the hypotenuse of a Pythagorean triple:
360-1173-1227 which is 3 times (120-391-409)

 

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1214 and Level 4

Even though I don’t tell you the order to consider the clues in today’s puzzle, you can still solve it. Just use logic and your knowledge of a standard 12 × 12 multiplication table to find its unique solution. Good luck!

Print the puzzles or type the solution in this excel file: 12 factors 1211-1220

Now I’ll share a few facts about the number 1214:

  • 1214 is a composite number.
  • Prime factorization: 1214 = 2 × 607
  • The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 1214 has exactly 4 factors.
  • Factors of 1214: 1, 2, 607, 1214
  • Factor pairs: 1214 = 1 × 1214 or 2 × 607
  • 1214 has no square factors that allow its square root to be simplified. √1214 ≈ 34.8425

1214 is the sum of six consecutive prime numbers:
191 + 193 + 197 + 199 + 211 + 223 = 1214

1204 and Level 4

Today’s puzzle looks like a giant times table with a big X in the middle. The factors for this times table are not in the usual places. Can you figure out where they all go?

Print the puzzles or type the solution in this excel file: 10-factors-1199-1210

Here are a few facts about the number 1204:

  • 1204 is a composite number.
  • Prime factorization: 1204 = 2 × 2 × 7 × 43, which can be written 1204 = 2² × 7 × 43
  • The exponents in the prime factorization are 2, 1, and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1)(1 + 1) = 3 × 2 × 2 = 12. Therefore 1204 has exactly 12 factors.
  • Factors of 1204: 1, 2, 4, 7, 14, 28, 43, 86, 172, 301, 602, 1204
  • Factor pairs: 1204 = 1 × 1204, 2 × 602, 4 × 301, 7 × 172, 14 × 86, or 28 × 43
  • Taking the factor pair with the largest square number factor, we get √1204 = (√4)(√301) = 2√301 ≈ 34.6987

1204 is the difference of two squares two different ways:
302² – 300² = 1204
50² – 36² = 1204

1194 and Level 4

The more multiplication facts you know, the easier these puzzles become. Working on these puzzles can help you learn the multiplication table better. Go ahead,  give this puzzle a try!

Print the puzzles or type the solution in this excel file: 12 factors 1187-1198

Here are a few facts about the number 1194:

  • 1194 is a composite number.
  • Prime factorization: 1194 = 2 × 3 × 199
  • The exponents in the prime factorization are 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 = 8. Therefore 1194 has exactly 8 factors.
  • Factors of 1194: 1, 2, 3, 6, 199, 398, 597, 1194
  • Factor pairs: 1194 = 1 × 1194, 2 × 597, 3 × 398, or 6 × 199
  • 1194 has no square factors that allow its square root to be simplified. √1194 ≈ 34.5543

1194 is the sum of consecutive prime numbers two ways:
131 + 137 + 139 + 149 + 151 + 157 + 163 + 167 = 1194
283 + 293 + 307 + 311 = 1194

1194 is palindrome 424 in BASE 17

 

1179 and Level 4

80 and 16 have just one common factor that will put only numbers from 1 to 10 in the first column and in the top row. Put those factors where they belong and use logic to figure out where to put the rest.

Print the puzzles or type the solution in this excel file: 10-factors-1174-1186

Now I tell you what I’ve learned about the number 1179:

  • 1179 is a composite number.
  • Prime factorization: 1179 = 3 × 3 × 131, which can be written 1179 = 3² × 131
  • The exponents in the prime factorization are 2 and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1) = 3 × 2  = 6. Therefore 1179 has exactly 6 factors.
  • Factors of 1179: 1, 3, 9, 131, 393, 1179
  • Factor pairs: 1179 = 1 × 1179, 3 × 393, or 9 × 131
  • Taking the factor pair with the largest square number factor, we get √1179 = (√9)(√131) = 3√131 ≈ 34.33657

I like the way 1179 looks in a couple other bases:
It’s 2233 in BASE 8 because 2(8³ + 8²) + 3(8 + 1) = 1179,
and 171 in BASE 31 because 31² + 7(31) + 1 = 1179

1166 and Level 4

Study the clues in this puzzle. Find the most logical place to start and begin there. Once you find all the factors you will see how amazing YOU are! You can do this!

Print the puzzles or type the solution in this excel file: 12 factors 1161-1173

Now I’ll share some information about the number 1166:

  • 1166 is a composite number.
  • Prime factorization: 1166 = 2 × 11 × 53
  • The exponents in the prime factorization are 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 = 8. Therefore 1166 has exactly 8 factors.
  • Factors of 1166: 1, 2, 11, 22, 53, 106, 583, 1166
  • Factor pairs: 1166 = 1 × 1166, 2 × 583, 11 × 106, or 22 × 53
  • 1166 has no square factors that allow its square root to be simplified. √1166 ≈ 34.14674

1166 is the hypotenuse of a Pythagorean triple:
616-990-1166 which is 22 times (28-45-53)

1153 Level 4 Pair of Glasses

Today’s puzzle reminds me of a pair of glasses. If I misplace my glasses, it can be difficult to find them, because I can’t see well without them.  But it shouldn’t be hard to see the logic in this level 4 puzzle. Give it a try. I think you will be pleasantly surprised.

Print the puzzles or type the solution in this excel file: 10-factors-1148-1160

Now let me see what I can tell you about the number 1153:

1153 is the sum of the thirteen prime numbers from 61 to 113.

Like every other prime number ending in 52, it is the sum of two squares:
33² + 8² = 1153

1153 is the hypotenuse of a Pythagorean triple:
528-1025-1153 calculated from 2(33)(8), 33² – 8², 33² + 8²

1153 is a palindrome in two other bases:
It’s 5C5 in BASE 14 (C is 12 base 10) because 5(14²) + 12(14) + 5(1) = 1153,
and 141 in BASE 32 because 32² + 4(32) + 1 = 1153

1139 and Level 4

The common factors of 30 and 48 are 1, 2, 3, and 6. The rules of a Find the Factors 1 – 12 puzzle require that only numbers from 1 to 12 go in either the first column or the top row. Each number can be used only once in each place. Which common factor of 30 and 48 must be chosen?

Print the puzzles or type the solution in this excel file: 12 factors 1134-1147

Here are some facts about the number 1139:

  • 1139 is a composite number.
  • Prime factorization: 1139 = 17 × 67
  • The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 1139 has exactly 4 factors.
  • Factors of 1139: 1, 17, 67, 1139
  • Factor pairs: 1139 = 1 × 1139 or 17 × 67
  • 1139 has no square factors that allow its square root to be simplified. √1139 ≈ 33.74907

1139 is the sum of seven/eleven consecutive primes:
149 + 151 + 157 + 163 + 167 + 173 + 179 = 1139
79 + 83 + 89 + 97 + 101 + 103 + 107 + 109 + 113 + 127 + 131 = 1139

1139 is the hypotenuse of a Pythagorean triple:
536-1005-1139 which is (8-15-17) times 67

1126 and Level 4

Since we are only using factors from 1 to 10, we have only one common factor of 12 and 9 to consider instead of two. Also, you will need to ask yourself, “Where is the only place ____ can fit in the first column (or the top row).” to solve this puzzle. Good Luck!

Print the puzzles or type the solution in this excel file: 10-factors-1121-1133

Here are some facts about the number 1126:

  • 1126 is a composite number.
  • Prime factorization: 1126 = 2 × 563
  • The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 1126 has exactly 4 factors.
  • Factors of 1126: 1, 2, 563, 1126
  • Factor pairs: 1126 = 1 × 1126 or 2 × 563
  • 1126 has no square factors that allow its square root to be simplified. √1126 ≈ 33.55592

I chuckled when I noticed that the first five digits of √1126 are all the factors in 1125’s prime factorization.

1126 is palindrome 1K1 in BASE 25 (K is 20 base 10) because 25² + 20(25) + 1 = 1126

1116 Can I Trick You With This Puzzle?

This is only a Level 4 puzzle, but can I trick you into making some assumptions about the puzzle’s factors? I bet I will trick a least a few people. Will you be one of them? If you don’t write a factor unless you are 100% sure it goes where you are putting it, I shouldn’t be able to trick you. Good luck with this one!

Print the puzzles or type the solution in this excel file: 12 factors 1111-1119

Now I’ll share some facts about the number 1116:

  • 1116 is a composite number.
  • Prime factorization: 1116 = 2 × 2 × 3 × 3 × 31, which can be written 1116 = 2² × 3² × 31
  • The exponents in the prime factorization are 2, 2 and 1. Adding one to each and multiplying we get (2 + 1)(2 + 1)(1 + 1) = 3 × 3 × 2 = 18. Therefore 1116 has exactly 18 factors.
  • Factors of 1116: 1, 2, 3, 4, 6, 9, 12, 18, 31, 36, 62, 93, 124, 186, 279, 372, 558, 1116
  • Factor pairs: 1116 = 1 × 1116, 2 × 558, 3 × 372, 4 × 279, 6 × 186, 9 × 124, 12 × 93, 18 × 62 or 31 × 36
  • Taking the factor pair with the largest square number factor, we get √1116 = (√36)(√31) = 6√31 ≈ 33.40659

1116 looks interesting when it is represented in these other bases:
It’s 13431 in BASE 5 because 1(5⁴) + 3(5³) + 4(5²) + 3(5) + 1(1) = 1116,
VV in BASE 35 (V is 31 base 10) because 31(35) + 31(1) = 31(36) = 1116, and
V0 in BASE 36 because 31(36) = 1116