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

 

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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

 

1106 and Level 4

Can you use logic to figure out where all the numbers from 1 to 10 need to go in both the first column and the top row so that this puzzle can become a multiplication table? Give it a try. It’s fun!

Print the puzzles or type the solution in this excel file: 10-factors-1102-1110

Here is some information about the number 1106:

  • 1106 is a composite number.
  • Prime factorization: 1106 = 2 × 7 × 79
  • 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 1106 has exactly 8 factors.
  • Factors of 1106: 1, 2, 7, 14, 79, 158, 553, 1106
  • Factor pairs: 1106 = 1 × 1106, 2 × 553, 7 × 158, or 14 × 79
  • 1106 has no square factors that allow its square root to be simplified. √1106 ≈ 33.25658

1106 is repdigit 222 in BASE 23 because 2(23² + 23+ 1) = 2(553) = 1106

1098 a Lucky Level 4 Puzzle?

You are lucky that this puzzle has some easy clues in it. You will have no problem getting started. Be warned, later on, you may not feel so lucky! I’m sure you can solve it if you keep with it.

Print the puzzles or type the solution in this excel file: 12 factors 1095-1101

Now, here are a few facts about the number 1098:

  • 1098 is a composite number.
  • Prime factorization: 1098 = 2 × 3 × 3 × 61, which can be written 1098 = 2 × 3² × 61
  • The exponents in the prime factorization are 1, 2, and 1. Adding one to each and multiplying we get (1 + 1)(2 + 1)(1 + 1) = 2 × 3 × 2 = 12. Therefore 1098 has exactly 12 factors.
  • Factors of 1098: 1, 2, 3, 6, 9, 18, 61, 122, 183, 366, 549, 1098
  • Factor pairs: 1098 = 1 × 1098, 2 × 549, 3 × 366, 6 × 183, 9 × 122, or 18 × 61,
  • Taking the factor pair with the largest square number factor, we get √1098 = (√9)(√122) = 3√122 ≈ 33.13608

This first fact from Stetson.edu uses only digits found in 1098. It makes 1098 look pretty lucky:
1098 = 11 + 0 + 999 + 88

1098 is the sum of four consecutive prime numbers:
269 + 271 + 277 + 281 = 1098

1098 is the hypotenuse of a Pythagorean triple:
198-1080-1098 which is 18 times (11-60-61)

1098 is a palindrome when it is written in three different bases:
It’s 2112 in BASE 8 because 2(8³) + 8² + 8 + 2(1) = 1098,
909 in BASE 11 because 9(11² + 1) = 9(122) = 1098, and it’s
666 in BASE 13. Oh my! How unlucky can you get? Why does it have two unlucky numbers, 666 and 13? Because 6(13² + 13 + 1) = 6(183) = 1098.

 

1090 and Level 4

This puzzle has both 54 and 56 as clues. Many people get the factors involved (6, 7, 8, 9) mixed up. Remember these two multiplication facts:
6 7 × 8 9 = 54
6 7 × 8 9 = 56
The closer factors make the bigger number.

Print the puzzles or type the solution in this excel file: 10-factors-1087-1094

Now I’ll share some information about the number 1090:

  • 1090 is a composite number.
  • Prime factorization: 1090 = 2 × 5 × 109
  • 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 1090 has exactly 8 factors.
  • Factors of 1090: 1, 2, 5, 10, 109, 218, 545, 1090
  • Factor pairs: 1090 = 1 × 1090, 2 × 545, 5 × 218, or 10 × 109
  • 1090 has no square factors that allow its square root to be simplified. √1090 ≈ 33.01515

1090 is the sum of the fourteen prime numbers from 47 to 107.

1090 is the sum of two squares two different ways:
27² + 19² = 1090
33² +  1² = 1090

1090 is the hypotenuse of four Pythagorean triples:
66-1088-1090 calculated from 2(33)(1), 33² –  1², 33² +  1²;
it is also 2 times (33-544-545),
368-1026-1090 calculated from 27² – 19² , 2(27)(19) , 27² + 19²;
it is also 2 times (184-513-545),
600-910-1090 which is 10 times (60-91-109)
654-872-1090 which is (3-4-5) times 218

1090 is a palindrome in two different bases:
It’s 1441 in BASE 9 because 1(9³) + 4(9²) + 4(9) + 1(1) = 1090
101 in BASE 33 because 33² + 1 = 1090