factor pairs

1295 Mystery Level

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This pinwheel-shaped puzzle is no little kid’s toy. The logic needed to solve it might be a mystery to see, but it is still there!

Print the puzzles or type the solution in this excel file: 12 factors 1289-1299

Here are some facts about the number 1295:

  • 1295 is a composite number.
  • Prime factorization: 1295 = 5 × 7 × 37
  • 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 1295 has exactly 8 factors.
  • Factors of 1295: 1, 5, 7, 35, 37, 185, 259, 1295
  • Factor pairs: 1295 = 1 × 1295, 5 × 259, 7 × 185, or 35 × 37
  • 1295 has no square factors that allow its square root to be simplified. √1295 ≈ 35.98611

Since 35 × 37 = 1295, we know that 1295 is one number less than 36².

1295 is the hypotenuse of FOUR Pythagorean triples:
399-1232-1295 which is 7 times (57-176-185)
420-1225-1295 which is 35 times (12-35-37)
728-1071-1295 which is 7 times (104-153-185)
777-1036-1295 which is (3-4-5) times 259

1294 and Level 6

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You will need to use multiplication facts from 1 to 12, logic, and perseverance to solve this tricky level 6 puzzle. Good luck!

Print the puzzles or type the solution in this excel file: 12 factors 1289-1299

Here are some facts about the number 1294:

  • 1294 is a composite number.
  • Prime factorization: 1294 = 2 × 647
  • 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 1294 has exactly 4 factors.
  • Factors of 1294: 1, 2, 647, 1294
  • Factor pairs: 1294 = 1 × 1294 or 2 × 647
  • 1294 has no square factors that allow its square root to be simplified. √1294 ≈ 35.97221

1294 is also the sum of the twenty prime numbers from 23 to 107.

1293 and Level 5

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Only factors from 1 to 12 are allowed in the factor pairs of the clues in these puzzles. Find a row or column with only one allowable common factor to start this puzzle. As you progress, factors for other rows or columns will be eliminated. Keep at it, and you will succeed!

Print the puzzles or type the solution in this excel file: 12 factors 1289-1299

Now I’ll share a few facts about the number 1293:

  • 1293 is a composite number.
  • Prime factorization: 1293 = 3 × 431
  • 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 1293 has exactly 4 factors.
  • Factors of 1293: 1, 3, 431, 1293
  • Factor pairs: 1293 = 1 × 1293 or 3 × 431
  • 1293 has no square factors that allow its square root to be simplified. √1293 ≈ 35.95831

1293 is palindrone 141 in BASE 34 because 34² + 4(34) + 1 = 1293

1292 and Level 4

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Finding the Factors in this puzzle will require you to use logic and you will get a bonus: your knowledge of the multiplication table will be a little better than it was before.

Print the puzzles or type the solution in this excel file: 12 factors 1289-1299

Now I’ll give you some information about today’s puzzle number:

  • 1292 is a composite number.
  • Prime factorization: 1292 = 2 × 2 × 17 × 19, which can be written 1292 = 2² × 17 × 19
  • 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 1292 has exactly 12 factors.
  • Factors of 1292: 1, 2, 4, 17, 19, 34, 38, 68, 76, 323, 646, 1292
  • Factor pairs: 1292 = 1 × 1292, 2 × 646, 4 × 323, 17 × 76, 19 × 68, or 34 × 38
  • Taking the factor pair with the largest square number factor, we get √1292 = (√4)(√323) = 2√323 ≈ 36.9444

1292 is the hypotenuse of a Pythagorean triple:
608-1140-1292 which is (8-15-17) times 76

1291 and Level 3

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If you think of the common factors of 25 and 55, then you have actually started to solve this puzzle! Start at the top of the puzzle and work your way down. Try it!

Print the puzzles or type the solution in this excel file: 12 factors 1289-1299

Here are some facts about the number 1291

  • 1291 is a prime number.
  • Prime factorization: 1291 is prime.
  • The exponent of prime number 1291 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 1291 has exactly 2 factors.
  • Factors of 1291: 1, 1291
  • Factor pairs: 1291 = 1 × 1291
  • 1291 has no square factors that allow its square root to be simplified. √1291 ≈ 35.93049

How do we know that 1291 is a prime number? If 1291 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1291 ≈ 35.9. Since 1291 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 or 31, we know that 1291 is a prime number.

1291 is also palindrome 1D1 in BASE 30 because 30² + 13(30) + 1 = 1291

 

1290 Multiplication Boomerang

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Do multiplication and division facts seem like something you threw out long ago but still come back to hit you? Perhaps this puzzle can help you get more familiar with those facts so they won’t hurt you so much anymore.

Print the puzzles or type the solution in this excel file: 12 factors 1289-1299

That was puzzle number 1290. Here are some facts about that number:

  • 1290 is a composite number.
  • Prime factorization: 1290 = 2 × 3 × 5 × 43
  • The exponents in the prime factorization are 1, 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 × 2 = 16. Therefore 1290 has exactly 16 factors.
  • Factors of 1290: 1, 2, 3, 5, 6, 10, 15, 30, 43, 86, 129, 215, 258, 430, 645, 1290
  • Factor pairs: 1290 = 1 × 1290, 2 × 645, 3 × 430, 5 × 258, 6 × 215, 10 × 129, 15 × 86, or 30 × 43
  • 1290 has no square factors that allow its square root to be simplified. √1290 ≈ 35.91657

1290 is the sum of two consecutive prime numbers:
643 + 647 = 1290

1290 is the hypotenuse of a Pythagorean triple:
774-1032-1290 which is (3-4-5) times 258

1289 and Level 1

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You might think this is a very easy puzzle, but for some people, it will be challenging, and will hopefully help them learn some multiplication facts better.

Print the puzzles or type the solution in this excel file: 12 factors 1289-1299

Since this is puzzle number 1289, I’ll share some facts about that number:

  • 1289 is a prime number.
  • Prime factorization: 1289 is prime.
  • The exponent of prime number 1289 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 1289 has exactly 2 factors.
  • Factors of 1289: 1, 1289
  • Factor pairs: 1289 = 1 × 1289
  • 1289 has no square factors that allow its square root to be simplified. √1289 ≈ 35.90265

How do we know that 1289 is a prime number? If 1289 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1289 ≈ 35.9. Since 1289 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 or 31, we know that 1289 is a prime number.

1289 is the sum of two squares:
35² + 8² = 1289

1289 is the hypotenuse of a Pythagorean triple:
560-1161-1289 calculated from 2(35)(8), 35² – 8², 35² + 8²

Here’s another way we know that 1289 is a prime number: Since its last two digits divided by 4 leave a remainder of 1, and 35² + 8² = 1289 with 35 and 8 having no common prime factors, 1289 will be prime unless it is divisible by a prime number Pythagorean triple hypotenuse less than or equal to √1289 ≈ 35.9. Since 1289 is not divisible by 5, 13, 17, or 29, we know that 1289 is a prime number.

1288 Mystery Puzzle

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How difficult is this mystery level puzzle? That is part of the mystery, but I assure you that if you use logic and basic multiplication facts you can find the unique solution.

Print the puzzles or type the solution in this excel file: 10-factors-1281-1288

That was puzzle #1288. Now I’ll tell you some facts about the number 1288.

  • 1288 is a composite number.
  • Prime factorization: 1288 = 2 × 2 × 2 × 7 × 23, which can be written 1288 = 2³ × 7 × 23
  • 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 1288 has exactly 16 factors.
  • Factors of 1288: 1, 2, 4, 7, 8, 14, 23, 28, 46, 56, 92, 161, 184, 322, 644, 1288
  • Factor pairs: 1288 = 1 × 1288, 2 × 644, 4 × 322, 7 × 184, 8 × 161, 14 × 92, 23 × 56, or 28 × 46
  • Taking the factor pair with the largest square number factor, we get √1288 = (√4)(√322) = 2√322 ≈ 37.88872

1288 has four factor pairs that contain only even factors so 1288 can be written as the difference of two squares four different ways:
323² – 321² = 1288
163² – 159² = 1288
53² – 39² = 1288
37² – 9² = 1288

 

1287 Mystery Level

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I’ve put twenty clues in this mystery level puzzle. Some of the factors will be easy to find, but some of them won’t be quite as easy. Use logic the entire time, and you will be able to solve it!

Print the puzzles or type the solution in this excel file: 10-factors-1281-1288

Now I’ll share some facts about the number 1287:

  • 1287 is a composite number.
  • Prime factorization: 1287 = 3 × 3 × 11 × 13, which can be written 1287 = 3² × 11 × 13
  • 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 1287 has exactly 12 factors.
  • Factors of 1287: 1, 3, 9, 11, 13, 33, 39, 99, 117, 143, 429, 1287
  • Factor pairs: 1287 = 1 × 1287, 3 × 429, 9 × 143, 11 × 117, 13 × 99, or 33 × 39
  • Taking the factor pair with the largest square number factor, we get √1287 = (√9)(√143) = 3√143 ≈ 35.87478

1287 is the hypotenuse of a Pythagorean triple:
495-1188-1287 which is (5-12-13) times 99

1286 and Level 6

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This level 6 puzzle can be solved by using logic and basic knowledge of the multiplication table. Stay focused, and you will get it done!

Print the puzzles or type the solution in this excel file: 10-factors-1281-1288

Here are a few facts about the number 1286:

  • 1286 is a composite number.
  • Prime factorization: 1286 = 2 × 643
  • 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 1286 has exactly 4 factors.
  • Factors of 1286: 1, 2, 643, 1286
  • Factor pairs: 1286 = 1 × 1286 or 2 × 643
  • 1286 has no square factors that allow its square root to be simplified. √1286 ≈ 35.86084

1286 is also the sum of six consecutive prime numbers:
197 + 199 + 211 + 223 + 227 + 229 = 1286