1196 and Level 6

In this puzzle, the permissible common factors of 48 and 72 are 6, 8, and 12. For clues 8 and 16, you can choose from common factors 2, 4, or 8. Which choices will make the puzzle work? I’m not telling, but I promise that the entire puzzle can be solved using logic and a basic knowledge of a 12×12 multiplication table. There is only one solution.

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

Here are some facts about the number 1196:

  • 1196 is a composite number.
  • Prime factorization: 1196 = 2 × 2 × 13 × 23, which can be written 1196 = 2² × 13 × 23
  • 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 1196 has exactly 12 factors.
  • Factors of 1196: 1, 2, 4, 13, 23, 26, 46, 52, 92, 299, 598, 1196
  • Factor pairs: 1196 = 1 × 1196, 2 × 598, 4 × 299, 13 × 92, 23 × 52, or 26 × 46
  • Taking the factor pair with the largest square number factor, we get √1196 = (√4)(√299) = 2√299 ≈ 34.58323

1196 is the hypotenuse of a Pythagorean triple:
460-1104-1196 which is (5-12-13) times 92

1196 is a palindrome in three different bases:
It’s 14241 in BASE 5,
838 in BASE 12, and
616 in BASE 14

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1182 A Unique Solution

Every Find the Factors puzzle I make has a unique solution. That fact is central to the logic needed to begin this particular puzzle. I hope it frustrates you a little, but not too much. Then when you finally solve it, it will be so much sweeter!

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

Here are some facts about the number 1182:

  • 1182 is a composite number.
  • Prime factorization: 1182 = 2 × 3 × 197
  • 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 1182 has exactly 8 factors.
  • Factors of 1182: 1, 2, 3, 6, 197, 394, 591, 1182
  • Factor pairs: 1182 = 1 × 1182, 2 × 591, 3 × 394, or 6 × 197
  • 1182 has no square factors that allow its square root to be simplified. √1182 ≈ 34.38023

1182 is the hypotenuse of a Pythagorean triple:
168-1170-1182 which is 6 times (28-195-197)

1182 is a palindrome in two bases:
It’s 606 in BASE 14 because 6(14²) + 6(1) = 6(197) = 1182,
and 2J2 in BASE 20 (J is 19 base 10) because 2(20²) + 19(20) + 2(1) = 1182

1169 and Level 6

The twelve clues in this puzzle make an attractive puzzle for you to solve. What factors go with those clues? Can you find the logic needed to figure this one out?

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

Now I’ll share what I’ve learned about the number 1169:

  • 1169 is a composite number.
  • Prime factorization: 1169 = 7 × 167
  • 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 1169 has exactly 4 factors.
  • Factors of 1169: 1, 7, 167, 1169
  • Factor pairs: 1169 = 1 × 1169 or 7 × 167
  • 1169 has no square factors that allow its square root to be simplified. √1169 ≈ 34.19064

1169 is the sum of consecutive prime numbers two different ways:
227+ 229 + 233+ 239+ 241 = 1169
383+ 389 + 397 = 1169

1169 is palindrome 5225 in BASE 6 because 5(6³) + 2(6²) + 2(6) + 5(1) = 1169

1157 and Level 6

The more you solve these puzzles, the easier most of them become. This one is no exception. Can you figure out the logic needed to make the first move?

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

Now I’ll share some facts about the number 1157:

  • 1157 is a composite number.
  • Prime factorization: 1157 = 13 × 89
  • 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 1157 has exactly 4 factors.
  • Factors of 1157: 1, 13, 89, 1157
  • Factor pairs: 1157 = 1 × 1157 or 13 × 89
  • 1157 has no square factors that allow its square root to be simplified. √1157 ≈ 34.0147

34² + 1² = 1157
31² + 14² = 1157

1157 is the hypotenuse of FOUR Pythagorean triples:
68-1155-1157 calculated from 2(34)(1), 34² – 1², 34² + 1²
445-1068-1157 which is (5-12-13) times 89
507-1040-1157 which is 13 times (39-80-89)
765-868-1157 calculated from 31² – 14², 2(31)(14), 31² + 14²

1157 is a palindrome in two different bases:
It’s 2D2 in BASE 21 (D is 13 base 10) because 2(21²) + 13(21) + 2(1) = 1157
101 in BASE 34 because 34² + 1 = 1157

1143 and Level 6

I hope you get “hooked” on factoring puzzles after you solve this one! It won’t be easy, but if you stick with it, you will be able to solve it. Good luck!

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

Now I’ll share some facts about the number 1143:

  • 1143 is a composite number.
  • Prime factorization: 1143 = 3 × 3 × 127, which can be written 1143 = 3² × 127
  • 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 1143 has exactly 6 factors.
  • Factors of 1143: 1, 3, 9, 127, 381, 1143
  • Factor pairs: 1143 = 1 × 1143, 3 × 381, or 9 × 127
  • Taking the factor pair with the largest square number factor, we get √1143 = (√9)(√127) = 3√127 ≈ 33.80828

1143 is repdigit 333 in BASE 19 because 3(19² + 19 + 1) = 3(381) = 1143

1130 and Level 6

Today’s puzzle has four sets of clues with two or more common factors. Which common factor should you choose in each case? Guessing and checking will only frustrate you. Study the puzzle instead. The clues work together to give ONE logical solution.

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

Now here is some information about the number 1130:

  • 1130 is a composite number.
  • Prime factorization: 1130 = 2 × 5 × 113
  • 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 1130 has exactly 8 factors.
  • Factors of 1130: 1, 2, 5, 10, 113, 226, 565, 1130
  • Factor pairs: 1130 = 1 × 1130, 2 × 565, 5 × 226, or 10 × 113
  • 1130 has no square factors that allow its square root to be simplified. √1130 ≈ 33.61547

1130 is the hypotenuse of FOUR Pythagorean triples:
150-1120-1130 which is 10 times (15-112-113)
552-986-1130 which is 2 times (276-493-565)
678-904-1130 which is (3-4-5) times 226
792-806-1130 which is 2 times (396-403-565)

1130 is also a leg in some Pythagorean triples including
1130-12744-12794 calculated from 2(113)(5), 113² – 5², 113² + 5²

1130 is palindrome 505 in BASE 15 because 5(15²) + 5(1) = 5(226) = 1130

1118 and Level 6

Each Level 6 puzzle has different logic needed to solve it. For this one, you will ask yourself over and over again, “Where is the only place ___ can go in the first column (or the top row)?” Just stick with it until all the numbers from 1 to 12 are in both of those places.

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

Now here’s a little about the number 1118:

  • 1118 is a composite number.
  • Prime factorization: 1118 = 2 × 13 × 43
  • 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 1118 has exactly 8 factors.
  • Factors of 1118: 1, 2, 13, 26, 43, 86, 559, 1118
  • Factor pairs: 1118 = 1 × 1118, 2 × 559, 13 × 86, or 26 × 43
  • 1118 has no square factors that allow its square root to be simplified. √1118 ≈ 33.43651

1118 is the hypotenuse of a Pythagorean triple:
430-1032-1118 which is (5-12-13) times 86

1118 is also a leg in one of this year’s Pythagorean triples!
1118-1680-2018 calculated from 2(43)(13), 43² – 13², 43² + 13²

1108 and Level 6

This level 6 puzzle has eleven clues. Which ones give away the most logical place for you to start it? I hope you have a lot of fun solving this one!

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

Now I’ll share some facts about the number 1108:

  • 1108 is a composite number.
  • Prime factorization: 1108 = 2 × 2 × 277, which can be written 1108 = 2² × 277
  • The exponents in the prime factorization are 1 and 2. Adding one to each and multiplying we get (2 + 1)(1 + 1) = 3 × 2  = 6. Therefore 1108 has exactly 6 factors.
  • Factors of 1108: 1, 2, 4, 277, 554, 1108
  • Factor pairs: 1108 = 1 × 1108, 2 × 554, or 4 × 277
  • Taking the factor pair with the largest square number factor, we get √1108 = (√4)(√277) = 2√277 ≈ 33.28663

1108 is the hypotenuse of a Pythagorean triple:
460-1008-1108 which is 4 times (115-252-277)

1108 is a palindrome when it is written in three other bases:
It’s 454 in BASE 16 because 4(16²) + 5(16) + 4(1) = 1108,
3E3 in BASE 17 (E is 14 base 10) because 3(17²) +14(17) +3(1) = 1108, and
1E1 in BASE 27 because 27² + 14(27) + 1 = 1108

1101 and Level 6

Which common factor of 6 and 24 will help you solve this puzzle? 2, 3, or 6?
Likewise, possible common factors of 8 and 4 are 1, 2, and 4, and for 48 and 36, you must choose between 4, 6, and 12.

In each case, only one choice will work with all the other clues in the puzzle.  You can figure out the correct choices and complete the entire puzzle by using logic. Good luck!

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

Here are a few facts about the number 1101:

Since it is made with a zero and exactly three identical numbers, it is divisible by 3.

  • 1101 is a composite number.
  • Prime factorization: 1101 = 3 × 367
  • 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 1101 has exactly 4 factors.
  • Factors of 1101: 1, 3, 367, 1101
  • Factor pairs: 1101 = 1 × 1101 or 3 × 367
  • 1101 has no square factors that allow its square root to be simplified. √1101 ≈ 33.18132

1101 is a palindrome when it is written in two other bases:
It’s 373 in BASE 18 because 3(18²) + 7(18) + 3(1) = 1101,
and 1J1 in BASE 25 (J is 19 in base 10) because 25² + 19(25) + 1 = 1101

1094 and Level 6

Should you choose 4 or 8 as the common factor of 32 and 16 in this puzzle?
Is 3 or 9 the common factor needed for 9 and 18?
And is 4 or 6 the common factor for 36 and 12 that will make this puzzle work?
In each of those cases, only one of those factors will work. Which one will it be?

The other clues will help you know where to logically start this puzzle. There is no need to guess and check. The entire puzzle can be solved using logic. Have fun!

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

Now I’ll tell you something about the number 1094:

  • 1094 is a composite number.
  • Prime factorization: 1094 = 2 × 547
  • 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 1094 has exactly 4 factors.
  • Factors of 1094: 1, 2, 547, 1094
  • Factor pairs: 1094 = 1 × 1094 or 2 × 547
  • 1094 has no square factors that allow its square root to be simplified. √1094 ≈ 33.07567

1094 is palindrome 2A2 in BASE 21 (A is 10 base 10) because 2(21²) + 10(21) + 2(1) = 1094