If you know the greatest common factor of 15 and 20, then you can begin to solve this puzzle. Since this is a level 3 puzzle, look at the clues starting at the top of the puzzle and work your way down, writing in the factors as you go. You can do this!

Print the puzzles or type the solution in this excel file: 10-factors-1242-1250

Now I’ll share some facts about the number 1245:

• 1245 is a composite number.
• Prime factorization: 1245 = 3 × 5 × 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 1245 has exactly 8 factors.
• Factors of 1245: 1, 3, 5, 15, 83, 249, 415, 1245
• Factor pairs: 1245 = 1 × 1245, 3 × 415, 5 × 249, or 15 × 83
• 1245 has no square factors that allow its square root to be simplified. √1245 ≈ 35.28456

1245 is also the hypotenuse of a Pythagorean triple:
747-996-1245 which is (3-4-5) times 249

If you can find the common factors of the clues in each row or column of this puzzle, then you can solve this puzzle. Be sure to only write numbers from 1 to 10 as those factors, and I’m sure you can succeed.

Print the puzzles or type the solution in this excel file: 10-factors-1242-1250

Here are some facts about the number 1244:

• 1244 is a composite number.
• Prime factorization: 1244 = 2 × 2 × 311, which can be written 1244 = 2² × 311
• 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 1244 has exactly 6 factors.
• Factors of 1244: 1, 2, 4, 311, 622, 1244
• Factor pairs: 1244 = 1 × 1244, 2 × 622, or 4 × 311
• Taking the factor pair with the largest square number factor, we get √1244 = (√4)(√311) = 2√311 ≈ 35.27038

1244 is the sum of the cubes of the first four triangular numbers:
1³ + 3³ + 6³ + 10³ =1244

1244 is a palindrome in a couple of different bases:
It’s 878 in BASE 12 and
282 in BASE 23

Here’s a great puzzle to help students figure out some division facts. That’s what they will have to do to find the factors from 1 to 10. Once they find those factors, they can complete the puzzle like it is a multiplication table.

Print the puzzles or type the solution in this excel file: 10-factors-1242-1250

Now I’ll share a few facts about the number 1243:

• 1243 is a composite number.
• Prime factorization: 1243 = 11 × 113
• 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 1243 has exactly 4 factors.
• Factors of 1243: 1, 11, 113, 1243
• Factor pairs: 1243 = 1 × 1243 or 11 × 113
• 1243 has no square factors that allow its square root to be simplified. √1243 ≈ 35.25621

1243 is also the hypotenuse of a Pythagorean triple:
165-1232-1243 which is 11 times (15-112-113)

If you use logic, you can figure out the solution to this puzzle. You will have to study all the clues just to know where to start, but I think you’ll find a lot of satisfaction in finding the solution.

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

Now I’ll share some facts about the number 1238:

• 1238 is a composite number.
• Prime factorization: 1238 = 2 × 619
• 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 1238 has exactly 4 factors.
• Factors of 1238: 1, 2, 619, 1238
• Factor pairs: 1238 = 1 × 1238 or 2 × 619
• 1238 has no square factors that allow its square root to be simplified. √1238 ≈ 35.18522

Because of its prime factors, I know that 1238 is part of only one Pythagorean triple:
1238-383160-383162

1238 is a palindrome in two other bases:
It’s 646 in BASE 14, and
it’s 383 in BASE 19.

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)