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

What is the greatest common factor of 28 and 63? If you know, then you can probably figure out this puzzle!

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Here are some facts about the number 1283:

• 1283 is a prime number.
• Prime factorization: 1283 is prime.
• The exponent of prime number 1283 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 1283 has exactly 2 factors.
• Factors of 1283: 1, 1283
• Factor pairs: 1283 = 1 × 1283
• 1283 has no square factors that allow its square root to be simplified. √1283 ≈ 35.81899

How do we know that 1283 is a prime number? If 1283 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1283 ≈ 35.8. Since 1283 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 or 31, we know that 1283 is a prime number.

1283 is the sum of the seventeen prime numbers from 41 to 109,
AND it is the sum of the thirteen primes from 71 to 131.

Can you find the factors from 1 to 10 that make the twelve clues in the puzzle the correct products for this scrambled multiplication table?

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

Here is some information about the number 1282:

• 1282 is a composite number.
• Prime factorization: 1282 = 2 × 641
• 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 1282 has exactly 4 factors.
• Factors of 1282: 1, 2, 641, 1282
• Factor pairs: 1282 = 1 × 1282 or 2 × 641
• 1282 has no square factors that allow its square root to be simplified. √1282 ≈ 35.80503

1282 is the sum of two squares:
29² +  21² = 1282

1282 is the hypotenuse of a primitive Pythagorean triple:
400-1218-1282 calculated from 29² –  21², 2(29)( 21), 29² +  21²

The 21, 29, and 400 above are related to another Pythagorean triple:
20-21-29 because 20² = 400, 21² = 441 and 29² = 841. Thus,
400 + 441 = 841. Pretty cool!

Can you write the numbers from 1 to 10 in the top row and the first column so that the given clues will make this puzzle work like a multiplication table? That’s how you solve the puzzle!

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

Now I’ll write a little bit about the number 1281:

• 1281 is a composite number.
• Prime factorization: 1281 = 3 × 7 × 61
• 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 1281 has exactly 8 factors.
• Factors of 1281: 1, 3, 7, 21, 61, 183, 427, 1281
• Factor pairs: 1281 = 1 × 1281, 3 × 427, 7 × 183, or 21 × 61
• 1281 has no square factors that allow its square root to be simplified. √1281 ≈ 35.79106

1281 is also the sum of consecutive prime numbers in two different ways:
167 + 173 + 179 + 181 + 191 + 193 + 197 = 1281
241 + 251 + 257 + 263 + 269 = 1281

1281 is the hypotenuse of a Pythagorean triple:
231-1260-1281 which is 21 times (11-60-61)

To me, today’s level 6 puzzle looks a little like a puppy dog. If you know or use a multiplication table, then with proper training, finding the factors of this puzzle will be no problem.

Print the puzzles or type the solution in this excel file: 12 factors 1271-1280

I’d like to tell you a little about the number 1280:

• 1280 is a composite number.
• Prime factorization: 1280 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5, which can be written 1280 = 2⁸ × 5
• The exponents in the prime factorization are 8 and 1. Adding one to each and multiplying we get (8 + 1)(1 + 1) = 9 × 2 = 18. Therefore 1280 has exactly 18 factors.
• Factors of 1280: 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 640, 1280
• Factor pairs: 1280 = 1 × 1280, 2 × 640, 4 × 320, 5 × 256, 8 × 160, 10 × 128, 16 × 80, 20 × 64, or 32 × 40
• Taking the factor pair with the largest square number factor, we get √1280 = (√256)(√5) = 16√5 ≈ 35.77709.

1280 is the sum of the fourteen prime numbers from 61 to 127. Do you know what those prime numbers are?

32² + 16² = 1280

1280 is the hypotenuse of a Pythagorean triple:
768-1024-1280 which is (3-4-5) times 256
That triple can also be calculated from 32² – 16², 2(32)(16), 32² + 16²

Since 1280 is the 5th multiple of 256, I would expect that a number close to 1280 would be the 500th number whose square root could be simplified. That number was 1275, just five numbers ago.

Try your hand at solving this level 4 puzzle. Your ability to do so might just surprise you!

Print the puzzles or type the solution in this excel file: 12 factors 1271-1280

Since this is my 1278th post, I’ll write a little bit about that number:

• 1278 is a composite number.
• Prime factorization: 1278 = 2 × 3 × 3 × 71, which can be written 1278 = 2 × 3² × 71
• The exponents in the prime factorization are 1, 2, and 1. Adding one to each and multiplying we get (1 + 1)(2 + 1)(1 + 1) = 2 × 3 × 2 = 12. Therefore 1278 has exactly 12 factors.
• Factors of 1278: 1, 2, 3, 6, 9, 18, 71, 142, 213, 426, 639, 1278
• Factor pairs: 1278 = 1 × 1278, 2 × 639, 3 × 426, 6 × 213, 9 × 142, or 18 × 71,
• Taking the factor pair with the largest square number factor, we get √1278 = (√9)(√142) = 3√142 ≈ 35.74913

1278 and the four numbers immediately preceding it are the smallest consecutive numbers for which 4 of the 5 numbers each have exactly 12 factors.

1278 is the sum of eight consecutive prime numbers:
139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 = 1278