V is for victory. Can you be victorious solving this puzzle? Write the numbers from 1 to 12 in both the first column and the top row so that the puzzle functions like a multiplication table with the given clues becoming the products of the factors you write. I’m sure you can do it if you stick with it!

Print the puzzles or type the solution in this excel file: 12 factors 1232-1241

Now I’ll tell you some facts about the number 1236:

• 1236 is a composite number.
• Prime factorization: 1236 = 2 × 2 × 3 × 103, which can be written 1236 = 2² × 3 × 103
• 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 1236 has exactly 12 factors.
• Factors of 1236: 1, 2, 3, 4, 6, 12, 103, 206, 309, 412, 618, 1236
• Factor pairs: 1236 = 1 × 1236, 2 × 618, 3 × 412, 4 × 309, 6 × 206, or 12 × 103
• Taking the factor pair with the largest square number factor, we get √1236 = (√4)(√309) = 2√309 ≈ 35.15679

1236 is the sum of consecutive prime numbers three rather interesting ways:

1. It is the sum of the twenty-two prime numbers from 13 to 103.
2. It is the sum of the eight prime numbers from 137 to 173.
   (137 + 139 + 149 + 151 + 157 + 163 + 167 + 173 = 1236)
3. It is also the sum of twin primes: 617 + 619 = 1236

Do you know the greatest common factor of 28 and 35? If you do, then you can solve this puzzle by writing each number from 1 to 12 in both the first column and the top row. Since this is a level 3 puzzle, you can begin with the clues at the top of the puzzle and work your way down cell by cell. Good luck!

Print the puzzles or type the solution in this excel file: 12 factors 1232-1241

Now I’ll share some facts about the number 1235:

• 1235 is a composite number.
• Prime factorization: 1235 = 5 × 13 × 19
• 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 1235 has exactly 8 factors.
• Factors of 1235: 1, 5, 13, 19, 65, 95, 247, 1235
• Factor pairs: 1235 = 1 × 1235, 5 × 247, 13 × 95, or 19 × 65
• 1235 has no square factors that allow its square root to be simplified. √1235 ≈ 35.14257

1235 is the hypotenuse of FOUR Pythagorean triples:
304-1197-1235 which is 19 times (16-63-65)
741-988-1235 which is (3-4-5) times 247
627-1064-1235 which is 19 times (33-56-65)
475-1140-1235 which is (5-12-13) times 95

This is my 1234th post, so today’s puzzle has been given that number. Whenever I see 12:34 on a clock, I always think about my husband’s Uncle Paul who really liked noticing that time because all possible clock digits are used and the digits are in order. I also like those digits because 12 = 3 × 4.

Print the puzzles or type the solution in this excel file: 12 factors 1232-1241

Here are some facts about the number 1234 some of which might surprise you:

• 1234 is a composite number.
• Prime factorization: 1234 = 2 × 617
• 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 1234 has exactly 4 factors.
• Factors of 1234: 1, 2, 617, 1234
• Factor pairs: 1234 = 1 × 1234 or 2 × 617
• 1234 has no square factors that allow its square root to be simplified. √1234 ≈ 35.12834

1234 is the sum of two squares:
35² + 3² = 1234

1234 is the hypotenuse of a Pythagorean triple:
210-1216-1234 calculated from 2(35)(3), 35² – 3², 35² + 3²
It is also 2 times (105-608-617)

Perhaps this puzzle is as difficult as a level 1 puzzle can be, but it is still not all that difficult. Nevertheless, if you can solve it, give yourself a big pat on the back.

Print the puzzles or type the solution in this excel file: 12 factors 1232-1241

Here are a few facts about the number 1233:

• 1233 is a composite number.
• Prime factorization: 1233 = 3 × 3 × 137, which can be written 1233 = 3² × 137
• 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 1233 has exactly 6 factors.
• Factors of 1233: 1, 3, 9, 137, 411, 1233
• Factor pairs: 1233 = 1 × 1233, 3 × 411, or 9 × 137
• Taking the factor pair with the largest square number factor, we get √1233 = (√9)(√137) = 3√137 ≈ 35.1141

Look at the numbers in this very cool but square fact about 1233:
12² + 33² = 1233

1233 is the hypotenuse of a Pythagorean triple:
792-945-1233 calculated from 2(33)(12), 33² – 12², 33² + 12²
It is also 9 times (88-105-137)

This level 5 puzzle has a row and a column with the exact same two clues. That ISN’T a good place to start this puzzle! Nevertheless, you can solve it, if you use logic and your knowledge of a basic 10 × 10 multiplication table. There is only one solution. Good luck!

Print the puzzles or type the solution in this excel file: 10-factors-1221-1231

Now I’ll share some information about the number 1228:

• 1228 is a composite number.
• Prime factorization: 1228 = 2 × 2 × 307, which can be written 1228 = 2² × 307
• 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 1228 has exactly 6 factors.
• Factors of 1228: 1, 2, 4, 307, 614, 1228
• Factor pairs: 1228 = 1 × 1228, 2 × 614, or 4 × 307
• Taking the factor pair with the largest square number factor, we get √1228 = (√4)(√307) = 2√307 ≈ 35.04283

1228 is repdigit 444 in BASE 17 because 4(17² + 17 + 1) = 4(307) = 1228