1144 Let’s Make a Factor Cake!

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Occasionally, I’ll put a factor cake on this blog, but until today, I haven’t really shown you how to MAKE a factor cake. I made this simple gif to show you how to make a factor cake from start to finish. You can watch it over and over again if you like. Just repeatedly divide by the smallest prime number divisor.

1144 Prime Factor Cake

make science GIFs like this at MakeaGif

Here’s more about the number 1144:

  • 1144 is a composite number.
  • Prime factorization: 1144 = 2 × 2 × 2 × 11 × 13, which can be written 1144 = 2³ × 11 × 13
  • 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 1144 has exactly 16 factors.
  • Factors of 1144: 1, 2, 4, 8, 11, 13, 22, 26, 44, 52, 88, 104, 143, 286, 572, 1144
  • Factor pairs: 1144 = 1 × 1144, 2 × 572, 4 × 286, 8 × 143, 11 × 104, 13 × 88, 22 × 52, or 26 × 44
  • Taking the factor pair with the largest square number factor, we get √1144 = (√4)(√286) = 2√286 ≈ 33.82307

1144 is obviously divisible by 11, but it isn’t so obvious that 1144 is the sum of the twenty-two prime numbers from 11 to 101.

1144 is the hypotenuse of a Pythagorean triple:
440-1056-1144 which is (5-12-13) times 88

1144 is palindrome 3223 in BASE 7 because 3(7³) + 2(7²) + 2(7) +3(1) = 1144

1143 and Level 6

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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

1142 and Level 5

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If you start in the right place, you will be able to solve this puzzle using logic and basic multiplication facts. Don’t get discouraged, if you make a mistake. I know you can figure this one out!

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

Here are some facts about the number 1142:

  • 1142 is a composite number.
  • Prime factorization: 1142 = 2 × 571
  • 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 1142 has exactly 4 factors.
  • Factors of 1142: 1, 2, 571, 1142
  • Factor pairs: 1142 = 1 × 1142 or 2 × 571
  • 1142 has no square factors that allow its square root to be simplified. √1142 ≈ 33.79349

1142 is a palindrome in three different bases:
It’s 949 in BASE 11 because 9(11²) + 4(11) + 9(1) = 1142,
3G3 in BASE 17 (G is 16 base 10) because 3(17²) + 16(17) + 3(1) = 1142,
and 2H2 in BASE 20 (H is 17 base 10) because 2(20²) + 17(20) + 2(1) = 1142

 

1141 is a Centered Hexagonal Number

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20³ – 19³ = 1141 so 1141 is the 20th centered hexagonal number:

Here’s more about the number 1141:

  • 1141 is a composite number.
  • Prime factorization: 1141 = 5 × 163
  • 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 1141 has exactly 4 factors.
  • Factors of 1141: 1, 5, 163, 1141
  • Factor pairs: 1141 = 1 × 1141 or 5 × 163
  • 1141 has no square factors that allow its square root to be simplified. √1141 ≈ 33.77869

5º(31²) + 5¹(31¹) + 5²(31º) = 1141

1141 is palindrome 181 in BASE 30 because 30² + 8(30) + 1 = 1141

1140 is the 18th Tetrahedral Number

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1140 is the 18th tetrahedral number because it satisfies this formula:
(18)(18+1)(18+2)/6 = 1140

It is the 18th tetrahedral number because it is the sum of the first 18 triangular numbers:

Since 18 is an even number, 1140 is the sum of the first 9 EVEN squares.

If the 1140 tiny squares in that graphic were cubes, they could be stacked into a tower with either a triangular base or a square base. Then we would see the beauty of this tetrahedral number.

We can see the number 1140 as well as ALL the previous tetrahedral numbers on this portion of Pascal’s Triangle. (They are the green squares.):

1140 has its place as the 3rd number (as well as the 17th number) on the 20th row of Pascal’s triangle because of this next formula:

Here are some other facts about the number 1140:

  • 1140 is a composite number.
  • Prime factorization: 1140 = 2 × 2 × 3 × 5 × 19, which can be written 1140 = 2² × 3 × 5 × 19
  • The exponents in the prime factorization are 2, 1, 1, and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1)(1 + 1)(1 + 1) = 2 × 3 × 2 × 2 = 24. Therefore 1140 has exactly 24 factors.
  • Factors of 1140: 1, 2, 3, 4, 5, 6, 10, 12, 15, 19, 20, 30, 38, 57, 60, 76, 95, 114, 190, 228, 285, 380, 570, 1140
  • Factor pairs: 1140 = 1 × 1140, 2 × 570, 3 × 380, 4 × 285, 5 × 228, 6 × 190, 10 × 114, 12 × 95, 15 × 76, 19 × 60, 20 × 57, or 30 × 38,
  • Taking the factor pair with the largest square number factor, we get √1140 = (√4)(√285) = 2√285 ≈ 33.76389

Here are some factor trees that use 11 of 1140’s factor pairs:

1140 is the sum of consecutive prime numbers two different ways:
179 + 181 + 191 + 193 + 197 + 199 = 1140,
569 + 571 = 1140

1140 is the hypotenuse of a Pythagorean triple:
684-912-1140 which is (3-4-5) times 228

1140 looks interesting when it is written in a couple other bases:
It’s palindrome 474 in BASE 16 because 4(16²) + 7(16) + 4(1) = 1140,
and it’s 330 in BASE 19 because 3(19²) + 3(19) = 3(19² + 19) = 3(19)(20) = 1140

1139 and Level 4

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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

1138 and Level 3

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There are two common factors of 10 and 14, but only one of them will put only numbers from 1 to 12 in the first column. Do you know what that factor is? If you do, figure out where to put the factors of 22, 66, 15 and so forth to make this puzzle function like a multiplication table. Each number from 1 to 12 can only appear once in the first column and once in the top row. You can do this!

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

Now I’d like to share some facts about the number 1138:

  • 1138 is a composite number.
  • Prime factorization: 1138 = 2 × 569
  • 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 1138 has exactly 4 factors.
  • Factors of 1138: 1, 2, 569, 1138
  • Factor pairs: 1138 = 1 × 1138 or 2 × 569
  • 1138 has no square factors that allow its square root to be simplified. √1138 ≈ 33.73426

33² + 7² = 1138

1138 is the hypotenuse of a Pythagorean triple:
462-1040-1138 calculated from 2(33)(7), 33² – 7², 33² + 7²

1137 and Level 2

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There’s no reason to let this puzzle tie you up in knots. Solving it will only require you to do a little thinking to make all the factors fall into place. I’m sure you can do it!

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

Here is a little information about the number 1137:

  • 1137 is a composite number.
  • Prime factorization: 1137 = 3 × 379
  • 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 1137 has exactly 4 factors.
  • Factors of 1137: 1, 3, 379, 1137
  • Factor pairs: 1137 = 1 × 1137 or 3 × 379
  • 1137 has no square factors that allow its square root to be simplified. √1137 ≈ 33.71943

1137 is a palindrome in three different bases:
It’s 10001110001 in BASE 2 because 2¹⁰ + 2⁶ + 2⁵ + 2⁴ + 2⁰ = 1137,
696 in BASE 13 because 6(13²) + 9(13) + 6(1) = 1137, and
393 in BASE 18 because 3(18²) + 9(18) + 3(1) = 1137

1136 and Level 1

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This puzzle has 20 clues to help you to know where to write the factors 1 to 12 in both the first column and the top row. After you find all the factors you can make the puzzle be a special type of multiplication table.

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

Here are a few facts about the number 1136:

  • 1136 is a composite number.
  • Prime factorization: 1136 = 2 × 2 × 2 × 2 × 71, which can be written 1136 = 2⁴ × 71
  • 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 1136 has exactly 10 factors.
  • Factors of 1136: 1, 2, 4, 8, 16, 71, 142, 284, 568, 1136
  • Factor pairs: 1136 = 1 × 1136, 2 × 568, 4 × 284, 8 × 142, or 16 × 71
  • Taking the factor pair with the largest square number factor, we get √1136 = (√16)(√71) = 4√71 ≈ 33.7046

1136 is palindrome 2C2 in BASE 21 (C is 12 base 10)
because 2(21²) + 12(21) + 2(1) = 1136

1135 is a Centered Triangular Number

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The reason 1135 is a centered triangular number is illustrated in this graphic:

(26×27 + 27×28 + 28×29)/2 = 1135 means that 1135 is the sum of the 26th, 27th, and 28th triangular numbers. The sum of three consecutive triangular numbers is always a centered triangular number.

Here are some more facts about the number 1135:

  • 1135 is a composite number.
  • Prime factorization: 1135 = 5 × 227
  • 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 1135 has exactly 4 factors.
  • Factors of 1135: 1, 5, 227, 1135
  • Factor pairs: 1135 = 1 × 1135 or 5 × 227
  • 1135 has no square factors that allow its square root to be simplified. √1135 ≈ 33.68976

1135 is the sum of the seventeen prime numbers from 31 to 103.
It is also the sum of three consecutive prime numbers:
373 + 379 + 383 = 1135

1135 is the hypotenuse of a Pythagorean triple:
681-908-1135 which is (3-4-5) times 227

1135 is a palindrome in two different bases:
It’s 7A7 in BASE 12 (A is 10 base 10) because 7(12²) + 10(12) + 7(1) = 1135,
and 1F1 in BASE 27 (F is 15 Base 10) because 27² + 15(27) + 1 = 1135