1321 Christmas Gift Puzzle

This puzzle looks like a gift because it is! You can fill out an entire multiplication table just from the 16 clues in this puzzle.

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1311 Little Square Candies

Here’s a puzzle made with some sweet squares. The nine clues in it are all you need to find the factors and complete the entire “mixed-up” multiplication table. 

Print the puzzles or type the solution in this excel file: 12 factors 1311-1319

Now I’ll write some facts about the number 1311:

  • 1311 is a composite number.
  • Prime factorization: 1311 = 3 × 19 × 23
  • 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 1311 has exactly 8 factors.
  • Factors of 1311: 1, 3, 19, 23, 57, 69, 437, 1311
  • Factor pairs: 1311 = 1 × 1311, 3 × 437, 19 × 69, or 23 × 57
  • 1311 has no square factors that allow its square root to be simplified. √1311≈ 36.20773

1311 is the sum of five consecutive prime numbers:
251 + 257 + 263 + 269 + 271 = 1311

1259 Graveyard Marker

This is the first of a week’s worth of Halloween Find the Factors puzzles. Graveyards are often associated with the holiday. Many graveyards have crosses marking the place where some dearly loved person was laid to rest. This puzzle isn’t very scary. Have fun solving it!

Print the puzzles or type the solution in this excel file: 10-factors-1259-1270

Now I’ll share some facts about the number 1259:

  • 1259 is a prime number.
  • Prime factorization: 1259 is prime.
  • The exponent of prime number 1259 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 1259 has exactly 2 factors.
  • Factors of 1259: 1, 1259
  • Factor pairs: 1259 = 1 × 1259
  • 1259 has no square factors that allow its square root to be simplified. √1259 ≈ 35.48239

How do we know that 1259 is a prime number? If 1259 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1259 ≈ 35.5. Since 1259 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 or 31, we know that 1259 is a prime number.

1259 is the sum of the twenty-five prime numbers from 5 to 103.

The number after 1259 has thirty-six factors. No wonder 1259 had to settle for 1 and itself being its only factors.

Between prime numbers 1237 and 1277, there are 39 numbers but only two of them are prime numbers. 1259 is one of them. Up to 1277 on the number line, no other segment of the same length has a lower incidence of prime numbers than that!

1251 and Level 1

Other than 1, what is the common factor of all the clues in this puzzle? Use that answer to fill in all the cells in the first column and the top row with the numbers from 1 to 12. then you will have the start of a different kind of multiplication table.

Print the puzzles or type the solution in this excel file: 12 factors 1251-1258

Now I’ll share some facts about the number 1251:

  • 1251 is a composite number.
  • Prime factorization: 1251 = 3 × 3 × 139, which can be written 1251 = 3² × 139
  • 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 1251 has exactly 6 factors.
  • Factors of 1251: 1, 3, 9, 139, 417, 1251
  • Factor pairs: 1251 = 1 × 1251, 3 × 417, or 9 × 139
  • Taking the factor pair with the largest square number factor, we get √1251 = (√9)(√139) = 3√139 ≈ 35.36948

1251 is also the sum of five consecutive prime numbers:
239 + 241 + 251 + 257 + 263 = 1251

1243 and Level 1

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)

 

1233 and Level 1

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)

1221 and Level 1

This puzzle is like a multiplication table with its factors in a different order. Can you figure out where the factors from 1 to 10 go in both the first column and the top row? Afterward, can you correctly fill in every cell of this mixed-up multiplication table?

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

Let me share some facts about the number 1221:

  • 1221 is a composite number.
  • Prime factorization: 1221 = 3 × 11 × 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 1221 has exactly 8 factors.
  • Factors of 1221: 1, 3, 11, 33, 37, 111, 407, 1221
  • Factor pairs: 1221 = 1 × 1221, 3 × 407, 11 × 111, or 33 × 37
  • 1221 has no square factors that allow its square root to be simplified. √1221 ≈ 34.94281

1 × 11 × 111 = 1221

1221 is the sum of five consecutive prime numbers:
233 + 239 + 241 + 251 + 257 = 1221

1221 is the hypotenuse of a Pythagorean triple:
396-1155-1221 which is 33 times (12-35-37)

Not only is 1221 a palindrome in base 10 but look at it in these other bases:
It’s 14341 in BASE 5,
5353 in BASE 6,
272 in BASE 23, and
it’s XX in BASE 36 because 33(36) + 33(1) = 33(37) = 1221

1211 and Level 1

Today we are reminded that the world can be a very complicated place. Today’s puzzle isn’t the least bit complicated. Just write the numbers from 1 to 12 in the first column and the top row so that the puzzle looks like a multiplication table (but with the factors not in their usual places.) Afterward, you can fill in the rest of the table. You can do this!

Print the puzzles or type the solution in this excel file: 12 factors 1211-1220

Now I’d like to share some information about the number 1211:

  • 1211 is a composite number.
  • Prime factorization: 1211 = 7 × 173
  • 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 1211 has exactly 4 factors.
  • Factors of 1211: 1, 7, 173, 1211
  • Factor pairs: 1211 = 1 × 1211 or 7 × 173
  • 1211 has no square factors that allow its square root to be simplified. √1211 ≈ 34.79943

1211 is the sum of the seventeen prime numbers from 37 to 107.
It is also the sum of seven consecutive primes:
157 + 163 + 167 + 173 + 179 + 181 + 191 = 1211

1211 is the hypotenuse of a Pythagorean triple:
364-1155-1211 which is 7 times (52-165-173)

1187 and Level 1

What is the biggest number that can divide all the clues in today’s puzzle without leaving a remainder? If you can answer that question, then you also know the greatest common factor of all those clues. It really is that simple. You can solve this puzzle!

Print the puzzles or type the solution in this excel file: 12 factors 1187-1198

Now I’ll share some information about the number 1187:

  • 1187 is a prime number.
  • Prime factorization: 1187 is prime.
  • The exponent of prime number 1187 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 1187 has exactly 2 factors.
  • Factors of 1187: 1, 1187
  • Factor pairs: 1187 = 1 × 1187
  • 1187 has no square factors that allow its square root to be simplified. √1187 ≈ 34.45287

How do we know that 1187 is a prime number? If 1187 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1187 ≈ 34.5. Since 1187 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 or 31, we know that 1187 is a prime number.

1187 is the sum of the nineteen prime numbers from 23 to 103.
It is also the sum of three consecutive primes:
389 + 397 + 401 = 1187

1174 and Level 1

I’ve given you just nine clues in this puzzle, but that’s enough to find all the factors AND complete the entire table. I’m serious. I really have given you sufficient information to find the one and only solution to this puzzle!

Print the puzzles or type the solution in this excel file: 10-factors-1174-1186

Now I’ll share some information about the number 1174:

  • 1174 is a composite number.
  • Prime factorization: 1174 = 2 × 587
  • 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 1174 has exactly 4 factors.
  • Factors of 1174: 1, 2, 587, 1174
  • Factor pairs: 1174 = 1 × 1174 or 2 × 587
  • 1174 has no square factors that allow its square root to be simplified. √1174 ≈ 34.26368

1174 is also the sum of the sixteen prime numbers from 41 to 107.