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

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

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

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

Level 5 puzzles can be tricky if you don’t carefully pick where you start, but you’re not going to let that discourage you, are you?

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

Here are a few facts about the number 1285:

• 1285 is a composite number.
• Prime factorization: 1285 = 5 × 257
• 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 1285 has exactly 4 factors.
• Factors of 1285: 1, 5, 257, 1285
• Factor pairs: 1285 = 1 × 1285 or 5 × 257
• 1285 has no square factors that allow its square root to be simplified. √1285 ≈ 35.8469

5(2⁸ + 1) = 1285. Look at the digits on both sides of that equation. They are the reason that 1285 is the 20th Friedman number.

1285 is the sum of three consecutive prime numbers:
421 + 431 + 433 = 1285

1285 is the sum of two squares two different ways:
33² + 14² = 1285
31² + 18² = 1285

1285 is the hypotenuse of FOUR Pythagorean triples:
160-1275-1285 which is 5 times (32-255-257)
637-1116-1285 calculated from 31² – 18², 2(31)(18), 31² + 18²
771-1028-1285 which is (3-4-5) times 257
893-924-1285 calculated from 33² – 14², 2(33)(14), 33² + 14²

Ten clues are in this puzzle. Two of them are 9’s and two of them are 10’s, but that doesn’t cause any problems, . . . .probably!

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

Here are some facts about the number 1284:

• 1284 is a composite number.
• Prime factorization: 1284 = 2 × 2 × 3 × 107, which can be written 1284 = 2² × 3 × 107
• 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 1284 has exactly 12 factors.
• Factors of 1284: 1, 2, 3, 4, 6, 12, 107, 214, 321, 428, 642, 1284
• Factor pairs: 1284 = 1 × 1284, 2 × 642, 3 × 428, 4 × 321, 6 × 214, or 12 × 107
• Taking the factor pair with the largest square number factor, we get √1284 = (√4)(√321) = 2√321 ≈ 35.83295

1284 is the sum of twin primes: 641 + 643 = 1284