1222 and Level 2

Can you write the numbers from 1 to 10 in both the first column and the top row of the table below so that the given clues are the multiplication products of the factors you wrote? There is only one solution, but I am sure that you can find it.

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

Now I’ll write a little bit about the number 1222:

  • 1222 is a composite number.
  • Prime factorization: 1222 = 2 × 13 × 47
  • 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 1222 has exactly 8 factors.
  • Factors of 1222: 1, 2, 13, 26, 47, 94, 611, 1222
  • Factor pairs: 1222 = 1 × 1222, 2 × 611, 13 × 94, or 26 × 47
  • 1222 has no square factors that allow its square root to be simplified. √1222 ≈ 34.95712

1222 is the hypotenuse of a Pythagorean triple:
470-1128-1222 which is (5-12-13) times 94

Advertisements

1212 and Level 2

I know you will find at least some of today’s puzzle to be easy, and maybe even all of it. Why not give it a try? You might just have fun solving it, too!

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

When we learn about the number 1212 we get to think about twelve a lot. 1212 has twelve factors and, of course, one of them is 12.

  • 1212 is a composite number.
  • Prime factorization: 1212 = 2 × 2 × 3 × 101, which can be written 1212 = 2² × 3 × 101
  • 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 1212 has exactly 12 factors.
  • Factors of 1212: 1, 2, 3, 4, 6, 12, 101, 202, 303, 404, 606, 1212
  • Factor pairs: 1212 = 1 × 1212, 2 × 606, 3 × 404, 4 × 303, 6 × 202, or 12 × 101
  • Taking the factor pair with the largest square number factor, we get √1212 = (√4)(√303) = 2√303 ≈ 34.81379

1212 is the sum of the fourteen prime numbers from 59 to 113.
It is also the sum of the twelve prime numbers from 73 to 131.
Do you know what all those prime numbers are?

1212 is the hypotenuse of a Pythagorean triple:
240-1188-1212 which is 12 times (20-99-101)

1202 and Level 2

I am certain that you can fill in the numbers 1 to 10 one time in both the top row and the first column so that this puzzle can become a multiplication table. All you have to do is give it an honest try.

Print the puzzles or type the solution in this excel file: 10-factors-1199-1210

Now I’ll write a few things about the number 1202:

  • 1202 is a composite number.
  • Prime factorization: 1202 = 2 × 601
  • 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 1202 has exactly 4 factors.
  • Factors of 1202: 1, 2, 601, 1202
  • Factor pairs: 1202 = 1 × 1202 or 2 × 601
  • 1202 has no square factors that allow its square root to be simplified. √1202 ≈ 34.66987

29² + 19² = 1202

1202 is the hypotenuse of a Pythagorean triple:
480-1102-1202 calculated from 29² – 19², 2(29)(19), 29² + 19²

2(24² + 5²) = 2(601) = 1202 so that Pythagorean triple can also be calculated from
2(2)(24)(5), 2(24² – 5²), 2(24² + 5²)

Try out both ways to get the triple!

 

1189 and Level 2

Some of the clues in this level 2 puzzle were also in the level 1 puzzle earlier this week. Can you remember their common factors and figure out the common factors for the other three sets of clues?

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

Here are some facts about the number 1189:

  • 1189 is a composite number.
  • Prime factorization: 1189 = 29 × 41
  • 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 1189 has exactly 4 factors.
  • Factors of 1189: 1, 29, 41, 1189
  • Factor pairs: 1189 = 1 × 1189 or 29 × 41
  • 1189 has no square factors that allow its square root to be simplified. √1189 ≈ 34.48188

33² + 10² = 1189
30² + 17² = 1189

1189 is the hypotenuse of FOUR Pythagorean triples:
261-1160-1189 which is 29 times (9-40-41)
611-1020-1189 calculated from 30² – 17², 2(30)(17), 30² + 17²
660-989-1189 calculated from 2(33)(10), 33² – 10², 33² + 10²
820-861-1189 which is (20-21-29) times 41

1189 is 10010100101 in BASE 2. That’s a nice pattern.
It’s also palindrome 1H1 in base 27 ( H is 17 base 10),
and palindrome 131 in BASE 33

1175 and Level 2

This level 2 puzzle will be quite useful in helping you recall all the multiplication facts. How many factors can you fill in on this puzzle without looking at a regular multiplication table? I congratulate you on all the ones you know.

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

Here are some facts about the number 1175:

  • 1175 is a composite number.
  • Prime factorization: 1175 = 5 × 5 × 47, which can be written 1175 = 5² × 47
  • 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 1175 has exactly 6 factors.
  • Factors of 1175: 1, 5, 25, 47, 235, 1175
  • Factor pairs: 1175 = 1 × 1175, 5 × 235, or 25 × 47
  • Taking the factor pair with the largest square number factor, we get √1175 = (√25)(√47) = 5√47 ≈ 34.27827

1175 is the hypotenuse of two Pythagorean triples:
705-940-1175 which is (3-4-5) times 235
329-1128-1175 which is (7-24-25) times 47

1175 is a palindrome in these other bases:
It’s 979 in BASE 11 because 9(11²) + 7(11) + 9(1) = 1175,
535 in BASE 15 because 5(15²) + 3(15) + 5(1) = 1175,
and 252 in BASE 23 because 2(23²) + 5(23) + 2(1) = 1175

1163 and Level 2

Can you write the numbers 1 to 12 in both the first column and the top row of this puzzle so those numbers and the clues function like a multiplication table? Sure you can!

Print the puzzles or type the solution in this excel file: 12 factors 1161-1173

Here is some information about the number 1163:

  • 1163 is a prime number.
  • Prime factorization: 1163 is prime.
  • The exponent of prime number 1163 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 1163 has exactly 2 factors.
  • Factors of 1163: 1, 1163
  • Factor pairs: 1163 = 1 × 1163
  • 1163 has no square factors that allow its square root to be simplified. √1163 ≈ 34.10279

How do we know that 1163 is a prime number? If 1163 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1163 ≈ 34.1. Since 1163 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 or 31, we know that 1163 is a prime number.

Prime number 1163 is also the sum of nine consecutive primes:
107 + 109 + 113 + 127 + 131 +137 + 139 + 149 + 151 = 1163

1149 and Level 2

Look at a typical 1 – 10 multiplication table. There is only one column on it that has the numbers 63, 27, and 72. What column is that? Put that column number in the cell in the top row above those numbers and you will have done the first step in completing this puzzle.  You will need to write the numbers from 1 to 10 in both the first column and the top row to solve this puzzle. Can you find the correct places to put each number?

Print the puzzles or type the solution in this excel file: 10-factors-1148-1160

Here are a few facts about the number 1149:

  • 1149 is a composite number.
  • Prime factorization: 1149 = 3 × 383
  • 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 1149 has exactly 4 factors.
  • Factors of 1149: 1, 3, 383, 1149
  • Factor pairs: 1149 = 1 × 1149 or 3 × 383
  • 1149 has no square factors that allow its square root to be simplified. √1149 ≈ 33.8969

1149 is palindrome 1D1 in BASE 28 (D is 13 base 10)
because 28² + 13(28) + 1 = 1149

1137 and Level 2

There’s no reason to let this puzzle tie you up in knots. Solving it will only require you to do a little thinking to make all the factors fall into place. I’m sure you can do it!

Print the puzzles or type the solution in this excel file: 12 factors 1134-1147

Here is a little information about the number 1137:

  • 1137 is a composite number.
  • Prime factorization: 1137 = 3 × 379
  • 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 1137 has exactly 4 factors.
  • Factors of 1137: 1, 3, 379, 1137
  • Factor pairs: 1137 = 1 × 1137 or 3 × 379
  • 1137 has no square factors that allow its square root to be simplified. √1137 ≈ 33.71943

1137 is a palindrome in three different bases:
It’s 10001110001 in BASE 2 because 2¹⁰ + 2⁶ + 2⁵ + 2⁴ + 2⁰ = 1137,
696 in BASE 13 because 6(13²) + 9(13) + 6(1) = 1137, and
393 in BASE 18 because 3(18²) + 9(18) + 3(1) = 1137

1113 and Level 2

If you’ve never solved a Find the Factors puzzle before, this level 2 puzzle will be a good one to try.  Just make sure each number 1 to 12 is written in the top row and the first column and that those numbers and the clues in the puzzle form a multiplication table. You can fill in the rest of the table later or not at all. Have fun!

Print the puzzles or type the solution in this excel file: 12 factors 1111-1119

Here is some information about the number 1113:

  • 1113 is a composite number.
  • Prime factorization: 1113 = 3 × 7 × 53
  • 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 1113 has exactly 8 factors.
  • Factors of 1113: 1, 3, 7, 21, 53, 159, 371, 1113
  • Factor pairs: 1113 = 1 × 1113, 3 × 371, 7 × 159, or 21 × 53
  • 1113 has no square factors that allow its square root to be simplified. √1113 ≈ 33.36165

1113 is the hypotenuse of a Pythagorean triple:
588-945-1113 which is 21 times (28-45-53)

1113 is made with three consecutive digits in these two consecutive bases:
It’s 789 in BASE 12 because 7(144) + 8(12) + 9(1) = 1113, and
it’s 678 in BASE 13 because 6(169) + 7(13) + 8(1) = 1113

1103 and Level 2

The fourteen clues you see in this puzzle are all you need to find all the factors from 1 to 10 and complete the multiplication table. Can you find all those factors?

Print the puzzles or type the solution in this excel file: 10-factors-1102-1110

Here are some facts about the number 1103:

  • 1103 is a prime number.
  • Prime factorization: 1103 is prime.
  • The exponent of prime number 1103 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 1103 has exactly 2 factors.
  • Factors of 1103: 1, 1103
  • Factor pairs: 1103 = 1 × 1103
  • 1103 has no square factors that allow its square root to be simplified. √1103 ≈ 33.21144

How do we know that 1103 is a prime number? If 1103 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1103 ≈ 33.2. Since 1103 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 or 31, we know that 1103 is a prime number.

1103 is the sum of the nineteen prime numbers from 19 to 101.

1103 is palindrome 191 in BASE 29 because 1(29²) + 9(29) + 1(1) = 1103