Number

1202 and Level 2

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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!

 

The factors of the hundred numbers just before 1201

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I’ve made a simple chart of the numbers from 1101 to 1200, but it’s packed with great information. It gives the prime factorization of each of those numbers and how many factors each of those numbers have. The numbers written with a pinkish hue are the ones whose square roots can be simplified. Notice that each of those numbers has an exponent in its prime factorization.

I didn’t make a horserace from the amounts of factors this time because it isn’t a very close race. Nevertheless, you can guess which number appears most often in the “Amount of Factors columns” and see if your number would have won the race.

Now I’ll share some information about the next number, 1201. Notice the last entry in the chart above. It had so many factors that there weren’t very many left for 1201 to have. . .

  • 1201 is a prime number.
  • Prime factorization: 1201 is prime.
  • The exponent of prime number 1201 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 1201 has exactly 2 factors.
  • Factors of 1201: 1, 1201
  • Factor pairs: 1201 = 1 × 1201
  • 1201 has no square factors that allow its square root to be simplified. √1201 ≈ 34.65545

How do we know that 1201 is a prime number? If 1201 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1201 ≈ 34.7. Since 1201 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 or 31, we know that 1201 is a prime number.

Even though it doesn’t have many factors, 1201 is still a fabulous number:

25² + 24² = 1201

1201 is the 25th Centered Square Number because 25² + 24² = 1201, and 24 and 25 are consecutive numbers:

1201 is the hypotenuse of a primitive Pythagorean triple:
49-1200-1201 calculated from 25² – 24², 2(25)(24), 25² + 24²

Here’s another way we know that 1201 is a prime number: Since its last two digits divided by 4 leave a remainder of 1, and 25² + 24² = 1201 with 25 and 24 having no common prime factors, 1201 will be prime unless it is divisible by a prime number Pythagorean triple hypotenuse less than or equal to √1201 ≈ 34.7. Since 1201 is not divisible by 5, 13, 17, or 29, we know that 1201 is a prime number.

1199 and Level 1

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Here’s a puzzle that even someone just learning to multiply and divide can solve. That means you can solve it, too!

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

Here are some facts about the number 1199:

  • 1199 is a composite number.
  • Prime factorization: 1199 = 11 × 109
  • 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 1199 has exactly 4 factors.
  • Factors of 1199: 1, 11, 109, 1199
  • Factor pairs: 1199 = 1 × 1199 or 11 × 109
  • 1199 has no square factors that allow its square root to be simplified. √1199 ≈ 34.62658

1199 is the sum of the fifteen prime numbers from 47 to 109. That last one just happens to be one of its prime factors, too!

1199 is the hypotenuse of a Pythagorean triple:
660-1001-1199 which is 11 times (60-91-109)

1199 looks cool in base 10, and it’s palindrome
2F2 in BASE 21 (F is 15 base 10)

 

1198 Challenge Puzzle

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You can solve this Find the Factors 1 – 10 puzzle if you use logic. Guessing and checking will likely only frustrate you. Go ahead and give logic a try!

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

Now I’ll share some facts about the number 1198:

  • 1198 is a composite number.
  • Prime factorization: 1198 = 2 × 599
  • 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 1198 has exactly 4 factors.
  • Factors of 1198: 1, 2, 599, 1198
  • Factor pairs: 1198 = 1 × 1198 or 2 × 599
  • 1198 has no square factors that allow its square root to be simplified. √1198 ≈ 34.61214

1198 is also palindrome 262 in BASE 23

1197 Mystery Level

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The first few moves needed to solve this puzzle might not be too hard, but soon enough it might get a bit tougher. Nevertheless, its one solution can be found using logic and an ordinary 12×12 multiplication table.

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

Here are facts about the number 1197:

  • 1197 is a composite number.
  • Prime factorization: 1197 = 3 × 3 × 7 × 19, which can be written 1197 = 3² × 7 × 19
  • 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 1197 has exactly 12 factors.
  • Factors of 1197: 1, 3, 7, 9, 19, 21, 57, 63, 133, 171, 399, 1197
  • Factor pairs: 1197 = 1 × 1197, 3 × 399, 7 × 171, 9 × 133, 19 × 63, or 21 × 57
  • Taking the factor pair with the largest square number factor, we get √1197 = (√9)(√133) = 3√133 ≈ 34.59769

1197 is the sum of these eleven consecutive prime numbers:
83 + 89 + 97 + 101 + 103 + 107 + 109 + 113 + 127 + 131 + 137 = 1197

1197 looks interesting to me when it is written in some other bases:
It’s 3330 in BASE 7 because 3(7³ + 7² + 7¹) = 3(399) = 1197,
and it’s 2255 in BASE 8.
It’s 999 in BASE 11, because 9(11² + 11 + 1) = 9(133) = 1197,
and it’s 1K1 in BASE 26 (K is 20 base 10)

 

1196 and Level 6

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In this puzzle, the permissible common factors of 48 and 72 are 6, 8, and 12. For clues 8 and 16, you can choose from common factors 2, 4, or 8. Which choices will make the puzzle work? I’m not telling, but I promise that the entire puzzle can be solved using logic and a basic knowledge of a 12×12 multiplication table. There is only one solution.

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

Here are some facts about the number 1196:

  • 1196 is a composite number.
  • Prime factorization: 1196 = 2 × 2 × 13 × 23, which can be written 1196 = 2² × 13 × 23
  • 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 1196 has exactly 12 factors.
  • Factors of 1196: 1, 2, 4, 13, 23, 26, 46, 52, 92, 299, 598, 1196
  • Factor pairs: 1196 = 1 × 1196, 2 × 598, 4 × 299, 13 × 92, 23 × 52, or 26 × 46
  • Taking the factor pair with the largest square number factor, we get √1196 = (√4)(√299) = 2√299 ≈ 34.58323

1196 is the hypotenuse of a Pythagorean triple:
460-1104-1196 which is (5-12-13) times 92

1196 is a palindrome in three different bases:
It’s 14241 in BASE 5,
838 in BASE 12, and
616 in BASE 14

1195 You Can Find the Answer in This Book

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The new school year is underway. Much may have been forgotten over the summer. If you don’t quite remember all the multiplication tables, this puzzle book can help you remember them AND help your brain grow. You might still find it a challenge, but that only makes it more fun!

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

Now I’ll share a few facts about the number 1195:

  • 1195 is a composite number.
  • Prime factorization: 1195 = 5 × 239
  • 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 1195 has exactly 4 factors.
  • Factors of 1195: 1, 5, 239, 1195
  • Factor pairs: 1195 = 1 × 1195 or 5 × 239
  • 1195 has no square factors that allow its square root to be simplified. √1195 ≈ 34.56877

1195 is also the hypotenuse of a Pythagorean triple:
717-956-1195 which is (3-4-5) times 239

1194 and Level 4

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The more multiplication facts you know, the easier these puzzles become. Working on these puzzles can help you learn the multiplication table better. Go ahead,  give this puzzle a try!

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

Here are a few facts about the number 1194:

  • 1194 is a composite number.
  • Prime factorization: 1194 = 2 × 3 × 199
  • 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 1194 has exactly 8 factors.
  • Factors of 1194: 1, 2, 3, 6, 199, 398, 597, 1194
  • Factor pairs: 1194 = 1 × 1194, 2 × 597, 3 × 398, or 6 × 199
  • 1194 has no square factors that allow its square root to be simplified. √1194 ≈ 34.5543

1194 is the sum of consecutive prime numbers two ways:
131 + 137 + 139 + 149 + 151 + 157 + 163 + 167 = 1194
283 + 293 + 307 + 311 = 1194

1194 is palindrome 424 in BASE 17

 

1193 Math Carnival Games

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During the last week of every month, there is a math education blog carnival happening somewhere in the blogosphere. This month it will happen on my blog! Why do I get to host it? I sent an email to Denise Gaskins who coordinates the carnival and requested the privilege. If you would like to host it in the future, let her know.

In the meantime, you can help me with my carnival. Math can be so much fun for kids from preschool age and even all the way up to high school. If you blog about that, I would love to include one or more of your posts in my carnival. You’ve poured your heart and soul into your posts, so why not promote it at no cost to you?  Don’t be shy! I want to read it, and other people will want to read it, too.

The deadline for submitting posts to my carnival is Friday, August 24th. There is a form for you to submit a link to your post on Denise Gaskins website. Then the following week you will be able to enjoy the carnival even more because of your participation!

Now it will be my pleasure to tell you a few facts about the number 1193:

  • 1193 is a prime number.
  • Prime factorization: 1193 is prime.
  • The exponent of prime number 1193 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 1193 has exactly 2 factors.
  • Factors of 1193: 1, 1193
  • Factor pairs: 1193 = 1 × 1193
  • 1193 has no square factors that allow its square root to be simplified. √1193 ≈ 34.53983

How do we know that 1193 is a prime number? If 1193 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1193 ≈ 34.5. Since 1193 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 or 31, we know that 1193 is a prime number.

1193 is the sum of five consecutive prime numbers:
229 + 233 + 239 + 241 + 251 = 1193

32² + 13² = 1193

1193 is the hypotenuse of a Pythagorean triple:
832-855-1193 calculated from 2(32)(13), 32² – 13², 32² + 13²

Here’s another way we know that 1193 is a prime number: Since its last two digits divided by 4 leave a remainder of 1, and 32² + 13² = 1193 with 32 and 13 having no common prime factors, 1193 will be prime unless it is divisible by a prime number Pythagorean triple hypotenuse less than or equal to √1193 ≈ 34.5. Since 1193 is not divisible by 5, 13, 17, or 29, we know that 1193 is a prime number.

1192 Experiential Learning Helps Students Understand Their Capacity

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Sara Van Der Werf inspired me last year with her post titled Why You Need a PLAY TABLE in your mathematics classroom ASAP. I’ve seen merit in using play to teach and learn mathematics for some time now. What Sara’s post did was make me long to be back in a mathematics classroom so I could have such a play table!

Last week I started working at the American Academy of Innovation, a charter school nearby that engages students in learning through projects and other activities.

Each member of the faculty was given the assignment to make something that reflects his or her teaching philosophy. Here’s the one I put together:

On my display, I included the words, “Experiential Learning Helps Students Understand Their Capacity.” That’s my teaching philosophy.

The wording I used was intentional.

  •  “Their” might refer to the students or to the geometric solids.
  • “Capacity” has two appropriate definitions stated so perfectly by Google in the screenshot below:
    1) the ability or power the students “have to do, experience, or understand something”, and 2) the maximum amount the geometric solids can contain.

The scattered rice symbolizes that these learning experiences can sometimes be messy. We will learn more if we aren’t afraid to make mistakes or a little mess.

I am so excited! I’ve taken all my math toys out of storage and will have an ever-changing play table in my classroom where students can play and learn mathematics. Thank you, Sara Van Der Werf for inspiring me!

Now I’ll write a little about the number 1192:

  • 1192 is a composite number.
  • Prime factorization: 1192 = 2 × 2 × 2 × 149, which can be written 1192 = 2³ × 149
  • The exponents in the prime factorization are 3 and 1. Adding one to each and multiplying we get (3 + 1)(1 + 1) = 4 × 2 = 8. Therefore 1192 has exactly 8 factors.
  • Factors of 1192: 1, 2, 4, 8, 149, 298, 596, 1192
  • Factor pairs: 1192 = 1 × 1192, 2 × 596, 4 × 298, or 8 × 149
  • Taking the factor pair with the largest square number factor, we get √1192 = (√4)(√298) = 2√298 ≈ 34.52535

1192 is the sum of two consecutive prime numbers:
593 + 599 = 1192

34² +  6² = 1192

1192 is the hypotenuse of a Pythagorean triple:
408-1120-1192 calculated from 2(34)( 6), 34² –  6², 34² +  6²
It is also 8 times (51-140-149)

1192 is a cool-looking 3322 in BASE 7