Factors

1167 and Level 5

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Will some of the tricky clues in this level 5 puzzle fool you? They won’t if you only write factors of which you are 100% sure. Always use logic. Never guess and check.

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

Now I’ll write a little bit about the number 1167:

  • 1167 is a composite number.
  • Prime factorization: 1167 = 3 × 389
  • 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 1167 has exactly 4 factors.
  • Factors of 1167: 1, 3, 389, 1167
  • Factor pairs: 1167 = 1 × 1167 or 3 × 389
  • 1167 has no square factors that allow its square root to be simplified. √1167 ≈ 34.16138

1167 is the hypotenuse of a Pythagorean triple:
567-1020-1167 which is 3 times (189-340-389)

1167 is palindrome 5D5 in BASE 14 (D is 13 base 10)
because 5(14²) + 13(14) + 5(1) = 1167

1166 and Level 4

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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)

1165 and Level 3

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Just because you start with the clues at the top of the puzzle and work down cell by cell to solve a level 3 puzzle doesn’t mean that you won’t have to do any thinking. Believe me, you will still have to THINK to solve this puzzle!

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

Now I’ll write a little bit about the number 1165:

  • 1165 is a composite number.
  • Prime factorization: 1165 = 5 × 233
  • 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 1165 has exactly 4 factors.
  • Factors of 1165: 1, 5, 233, 1165
  • Factor pairs: 1165 = 1 × 1165 or 5 × 233
  • 1165 has no square factors that allow its square root to be simplified. √1165 ≈ 34.132096

34² + 3² = 1165
29² + 18² = 1165

1165 is the hypotenuse of FOUR Pythagorean triples:
204-1147-1165 calculated from 2(34)(3), 34² – 3², 34² + 3²
517-1044-1165 calculated from 29² – 18², 2(29)(18), 29² + 18²
525-1040-1165 which is 5 times (105-208-233)
699-932-1165 which is (3-4-5) times 233

1164 Mathematics at Corvin Castle

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In the forests of Transylvania in what is now Hunedoara, Romania, a large, beautiful, well-restored, and fascinating castle awaits. At Corvin Castle, you can see how enemies were tortured and royal friends were entertained in the days of kings and knights. However, the room that intrigued me the most was full of mathematics. I didn’t take a picture of every geometric shape that graced its walls; I only took a few. You will have to go there yourself to see all the wonderful mathematical artwork. I thoroughly enjoyed myself!

I knew that fellow mathematical puzzle maker, Simona Prilogan,  was from Romania, but I didn’t realize until after I returned home that this castle is in her hometown! She recently wrote about the castle and her experience growing up in Hunedoara. As a child, she was chosen to write a poem about Romania’s president and present the poem at this very castle.

Now I’ll tell you a little something about the number 1164:

  • 1164 is a composite number.
  • Prime factorization: 1164 = 2 × 2 × 3 × 97, which can be written 1164 = 2² × 3 × 97
  • 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 1164 has exactly 12 factors.
  • Factors of 1164: 1, 2, 3, 4, 6, 12, 97, 194, 291, 388, 582, 1164
  • Factor pairs: 1164 = 1 × 1164, 2 × 582, 3 × 388, 4 × 291, 6 × 194, or 12 × 97
  • Taking the factor pair with the largest square number factor, we get √1164 = (√4)(√291) = 2√291 ≈ 34.117444

1164 is the sum of consecutive prime numbers FOUR different ways:
It’s the sum of the eighteen prime numbers from 29 to 103.
97 + 101 + 103 + 107 + 109 + 113 + 127 + 131+ 137 + 139 = 1164; that’s ten consecutive primes,
281 + 283 + 293 + 307 = 1164; that’s four consecutive primes, and
577 + 587 = 1164; that’s two consecutive primes.

1164 is the hypotenuse of a Pythagorean triple:
780-864-1164 which is 12 times (65-72-97)

1164 is palindrome 969 in BASE 11 because 9(11²) + 6(11) + 9(1) = 1164,
and it’s 345 in BASE 19 because 3(19²) + 4(19) + 5(1) = 1164

 

1162 Is a Pentagonal Number

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1162 is the 28th pentagonal number because (3(28²) – 28)/2 = 1162. I created the graphic below so you can see all the pentagonal numbers up to 1162 and figure out why all of them are called pentagonal numbers.

Here’s more about the number 1162:

  • 1162 is a composite number.
  • Prime factorization: 1162 = 2 × 7 × 83
  • 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 1162 has exactly 8 factors.
  • Factors of 1162: 1, 2, 7, 14, 83, 166, 581, 1162
  • Factor pairs: 1162 = 1 × 1162, 2 × 581, 7 × 166, or 14 × 83
  • 1162 has no square factors that allow its square root to be simplified. √1162 ≈ 34.08812

1162 is a palindrome in three bases:
It’s 343 in BASE 19 because 3(19²) + 4(19) + 3(1) = 1162,
2I2 in BASE 20 (I is 18 base 10) because 2(20²) + 18(20) + 2(1) = 1162, and
1G1 in BASE 27 (G is 16 base 10) because 27² + 16(27) + 1 = 1162

1161 and Level 1

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Solving this puzzle will help you review the multiplication table. Knowing the multiplication table inside and out will be a big PLUS in your life. It will save you so much time in all your mathematics classes!

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

Here is some information about the number 1161:

  • 1161 is a composite number.
  • Prime factorization: 1161 = 3 × 3 × 3 × 43, which can be written 1161 = 3³ × 43
  • The exponents in the prime factorization are 3 and 1. Adding one to each and multiplying we get (3 + 1)(1 + 1) = 4 × 2 = 8. Therefore 1161 has exactly 8 factors.
  • Factors of 1161: 1, 3, 9, 27, 43, 129, 387, 1161
  • Factor pairs: 1161 = 1 × 1161, 3 × 387, 9 × 129, or 27 × 43
  • Taking the factor pair with the largest square number factor, we get √1161 = (√9)(√129) = 3√129 ≈ 34.07345

1161 is the sum of the first twenty-six prime numbers. That’s all the primes from 2 to 101.

1161 is a palindrome in a couple of bases:
It’s 10010001001 in BASE 2 because 2¹⁰ + 2⁷ + 2³ + 2⁰ = 1161 and
1B1 in BASE 29 (B is 11 base 10) because 29² + 11(29) + 1 = 1161

1160 Find the Factors Challenge

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I love this particular puzzle. I had so much fun figuring out the logic. It’s a little bit complicated, but once you figure out the first move, it shouldn’t take too long to figure out most of the rest of the puzzle. Do give it a try!

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

Here are some facts about the number 1160:

  • 1160 is a composite number.
  • Prime factorization: 1160 = 2 × 2 × 2 × 5 × 29, which can be written 1160 = 2³ × 5 × 29
  • The exponents in the prime factorization are 3, 1, and 1. Adding one to each and multiplying we get (3 + 1)(1 + 1)(1 + 1) = 4 × 2 × 2 = 16. Therefore 1160 has exactly 16 factors.
  • Factors of 1160: 1, 2, 4, 5, 8, 10, 20, 29, 40, 58, 116, 145, 232, 290, 580, 1160
  • Factor pairs: 1160 = 1 × 1160, 2 × 580, 4 × 290, 5 × 232, 8 × 145, 10 × 116, 20 × 58, or 29 × 40
  • Taking the factor pair with the largest square number factor, we get √1160 = (√4)(√290) = 2√290 ≈ 34.05877

26² + 22² = 1160
34² +  2² = 1160

1160 is the hypotenuse of FOUR Pythagorean triples:
136-1152-1160 which is 8 times (17-144-145)
(It can also be calculated from 2(34)(2), 34² –  2², 34² +  2²)
192-1144-1160 which is 8 times (24-143-145)
(It can also be calculated from 26² – 22², 2(26)(22), 26² + 22²)
696-928-1160 which is (3-4-5) times 232
800-840-1160 which is (20-21-29) times 40

1160 is a palindrome when it is written in these three bases:
It’s 808 in BASE 12 because 8(12²) + 8(1) = 8(145) = 1160,
525 in BASE 15 because 5(15²) + 2(15) + 5(1) = 1160, and
404 in BASE 17 because 4(17²) + 4(1) = 4(290) = 1160

1159 Mystery Level

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This mysterious multiplication table does not have its factors in the usual places. Can you use logic to figure out where the factors from 1 to 10 go so that the given clues belong where they are?

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

What can I tell you about the number 1159?

  • 1159 is a composite number.
  • Prime factorization: 1159 = 19 × 61
  • 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 1159 has exactly 4 factors.
  • Factors of 1159: 1, 19, 61, 1159
  • Factor pairs: 1159 = 1 × 1159 or 19 × 61
  • 1159 has no square factors that allow its square root to be simplified. √1159 ≈ 34.04409

1159 is the sum of the twenty-five prime numbers from 3 to 101.

1159 is the hypotenuse of a Pythagorean triple:
209-1140-1159 which is 19 times (11-60-61)

1158 Mystery Level

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The twelve clues in this puzzle are easy to see, but solving the mystery of the puzzle might not be so easy. The clues work together to point to particular factors. Can you figure out where they all go?

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

Now I’ll write a little bit about the number 1158:

  • 1158 is a composite number.
  • Prime factorization: 1158 = 2 × 3 × 193
  • 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 1158 has exactly 8 factors.
  • Factors of 1158: 1, 2, 3, 6, 193, 386, 579, 1158
  • Factor pairs: 1158 = 1 × 1158, 2 × 579, 3 × 386, or 6 × 193
  • 1158 has no square factors that allow its square root to be simplified. √1158 ≈ 34.0294

1158 is the hypotenuse of a Pythagorean triple:
570-1008-1158 which is 6 times (95-168-193)

1158 is 123 in BASE 33 because 33² + 2(33) + 3(1) = 1158

1157 and Level 6

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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