factor pairs

1172 Mystery Puzzle

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There are thirteen clues in this Mystery Level Find the Factors 1 – 12 puzzle. Will those thirteen clues bring you good luck or bad? The logic needed to solve the puzzle may be a bit complicated, but if you stick with it, you will figure it out. Good luck to you!

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

Let me share some facts about the number 1172:

  • 1172 is a composite number.
  • Prime factorization: 1172 = 2 × 2 × 293, which can be written 1172 = 2² × 293
  • 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 1172 has exactly 6 factors.
  • Factors of 1172: 1, 2, 4, 293, 586, 1172
  • Factor pairs: 1172 = 1 × 1172, 2 × 586, or 4 × 293
  • Taking the factor pair with the largest square number factor, we get √1172 = (√4)(√293) = 2√293 ≈ 34.23449

1172 is the sum of six consecutive prime numbers:
181 + 191 + 193 + 197 + 199 + 211 = 1172

34² + 4² = 1172

1172 is the hypotenuse of a Pythagorean triple:
272-1140-1172 calculated from 2(34)(4), 34² – 4², 34² + 4²
It is also 4 times (68-285-293)

1172 is a palindrome in a couple of bases:
It’s 818 in BASE 12 because 8(12²) + 1(12) + 8(1) = 1172,
and 494 in BASE 16 4(16²) + 9(16) + 4(1) = 1172

1170 Factor Trees

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1170 is one of those numbers with twenty-four factors. Why does it have so many? Because of its prime factorization. You can find a number’s prime factorization by making a factor tree. Here are eleven different factor trees for 1170. Each one of them produces the same prime factorization: 1170 = 2 × 3² × 5 × 13

  • 1170 is a composite number.
  • Prime factorization: 1170 = 2 × 3 × 3 × 5 × 13, which can be written 1170 = 2 × 3² × 5 × 13
  • The exponents in the prime factorization are 1, 2, 1, and 1. Adding one to each and multiplying we get (1 + 1)(2 + 1)(1 + 1)(1 + 1) = 2 × 3 × 2 × 2 = 24. Therefore 1170 has exactly 24 factors.
  • Factors of 1170: 1, 2, 3, 5, 6, 9, 10, 13, 15, 18, 26, 30, 39, 45, 65, 78, 90, 117, 130, 195, 234, 390, 585, 1170
  • Factor pairs: 1170 = 1 × 1170, 2 × 585, 3 × 390, 5 × 234, 6 × 195, 9 × 130, 10 × 117, 13 × 90, 15 × 78, 18 × 65, 26 × 45, or 30 × 39
  • Taking the factor pair with the largest square number factor, we get √1170 = (√9)(√130) = 3√130 ≈ 34.20526

33² +  9² = 1170
27² +  21² = 1170

1170 is also the hypotenuse of FOUR Pythagorean triples:
288-1134-1170 calculated from 27² –  21², 2(27)(21), 27² +  21²
450-1080-1170 which is (5-12-13) times 90
594-1008-1170 calculated from 2(33)( 9), 33² –  9², 33² +  9²
702-936-1170 which is (3-4-5) times 234

1170 is 102102 in BASE 4 because 4⁵ + 2(4³) +4² + 2(1) = 1170,
and it’s repdigit 2222 in BASE 8 because 2(8³ + 8² + 8¹ + 8⁰) = 2(585) = 1170

1169 and Level 6

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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

1168 Sosto Museum Village School Room

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During our recent visit to Nyíregyháza, Hungary we visited the Sosto Museum Village. One of my favorite places there was this school room.

The room was roped off so I had to settle for this shot from the doorway. Let me tell you what I see in this picture.

On the right of the picture is an abacus. As a lover of mathematics, I have to love that there was an abacus in the classroom.

At the top of the page near the center is a map of Szabolcs and Ung Counties. Ung county was where my husband’s maternal grandfather was born and was only about 75 km from this museum village. I like to think that his grandfather’s classroom might have been just like this one.

I love the ceiling with its wooden beams as well as the desks and other wood furnishings in the room. My husband’s paternal grandfather was a cabinet maker. The second cousins we met in Romania informed us that this grandfather made the desks at their school. Even though that school was far away from this museum village, I imagine that the desks he made looked much like these.

In a different classroom, we found this mathematics book. We could walk up and look at it quite easily, but we couldn’t turn any of the pages because it was behind glass. I apologize for the glare from the glass. They don’t make arithmetic books like this anymore!

One of the classrooms had this guide for reading and writing the alphabet.

Some other pictures of the museum village can be found here. I took other pictures, but this is enough for this post. I recommend going to Sosto Museum should you ever travel to Hungary.

Now I’ll write a little about the number 1168:

  • 1168 is a composite number.
  • Prime factorization: 1168 = 2 × 2 × 2 × 2 × 73, which can be written 1168 = 2⁴ × 73
  • The exponents in the prime factorization are 4 and 1. Adding one to each and multiplying we get (4 + 1)(1 + 1) = 5 × 2 = 10. Therefore 1168 has exactly 10 factors.
  • Factors of 1168: 1, 2, 4, 8, 16, 73, 146, 292, 584, 1168
  • Factor pairs: 1168 = 1 × 1168, 2 × 584, 4 × 292, 8 × 146, or 16 × 73
  • Taking the factor pair with the largest square number factor, we get √1168 = (√16)(√73) = 4√73 ≈ 34.17601

1168 is the hypotenuse of a Pythagorean triple:
768-880-1168 which is 16 times (48-55-73)

1168 is palindrome 292 in BASE 22 because 2(22²) + 9(22) + 2(1) = 1168

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