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lmost all of the “counting numbers” (1, 2, 3, 4, 5, etc.) can be placed into one of two categories: prime or composite. Prime numbers have exactly two positive factors – one and themselves. Composite numbers have more than two positive factors.

The Number 1:

I say almost because 1 fits in neither of these two categories! By definition, 1 is not prime nor is it composite.

A prime number must have exactly two positive factors. 1 has only one factor (which is 1) so 1 is not a prime number. A composite number has to have more than two positive factors. Again, 1 does not meet that requirement with its singular factor so 1 cannot be a composite number. 1 therefore, is a special case. It is the only “counting number” that is neither prime nor composite.

Even and Odd Primes:

Most prime numbers are odd: 3, 5, 7, 23, etc. These are called odd primes.

2 however, an exception to the rule. The number 2 is the only even prime number. 2 has exactly two positive factors (2 and 1), therefore it is a prime number. All other even numbers, also have 2 as a factor which means they have at least three positive factors and are therefore not prime.

Take 6 for example. The positive factors of 6 are 1, 6, 2 and 3. Having four positive factors makes 6 a composite number.

How about 10? The positive factors of 10 are 1, 10, 2 and 5. Again, having four positive factors makes 10 a composite number.

Every single even number larger than 2 has at least four positive factors. These factors are always 1, the number itself, 2 and its partner. Many even numbers have even more! Therefore, you can know that all even numbers larger than 2 are composite numbers.

4th Grade Common Core Math: Daily Practice Workbook Part I: Multiple Choice
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This book is your comprehensive workbook for 4th Grade Math. By practicing and mastering this entire workbook, your child will become very familiar and comfortable with the state math exam and common core standards. This 4th Grade Common Core Math Workbook (Multiple Choice) includes: 20 Weeks of Daily Multiple Choice Practice Weekly Assessments State Aligned Common Core Curriculum End of Year Assessment This book has the following topics covered: Week 1 - Place value and comparison symbols Week 2 - Rounding numbers Week 3 - Division problems Week 4 - Multiplication and division problems Week 5 - Multi-step word problems Week 6 - Patterns and rules Week 7 - Fraction comparisons Week 8 - Adding and subtraction fractions Week 9 - Multiplying fractions by a whole number Week 10 - Denominators with 10 or 100 Week 11 - Comparing decimal numbers Week 12 - Measurement units Week 13 - Real world word problems Week 14 - Tables and charts Week 15 - Angles Week 16 - Angles (continued) Week 17 - Angles (continued) Week 18 - Right, acute, and obtuse angles Week 19 - Geometric shapes Week 20 - Line of symmetry End of Year Assessment For practice with Free Response questions, be sure to check out Part II of our workbook titled: 4th Grade Common Core Math: Daily Practice Workbook - Part II: Free Response | 1000+ Practice Questions and Video Explanations Each question is labeled with the specific common core standard so both parents and teachers can use this workbook for their student(s). This workbook takes the Common Core State Standards and divides them up among 20 weeks. By working on these problems on a daily basis, students will be able to (1) find any deficiencies in their understanding and/or practice of math and (2) have small successes each day that will build competence and confidence in their abilities.
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4th Grade Common Core Math: Daily Practice Workbook Part II: Free Response
$19.99
This book is your comprehensive workbook for 4th Grade Common Core Math. By practicing and mastering this entire workbook, your child will become very familiar and comfortable with the state math exam and common core standards. This 4th Grade Common Core Math Workbook (Free Response) includes: 20 Weeks of Daily Free Response Practice Weekly Assessments State Aligned Common Core Curriculum End of Year Assessment This book has the following topics covered: Week 1 - Place value and comparison symbols Week 2 - Rounding numbers Week 3 - Division problems Week 4 - Multiplication and division problems Week 5 - Multi-step word problems Week 6 - Patterns and rules Week 7 - Fraction comparisons Week 8 - Adding and subtraction fractions Week 9 - Multiplying fractions by a whole number Week 10 - Denominators with 10 or 100 Week 11 - Comparing decimal numbers Week 12 - Measurement units Week 13 - Real world word problems Week 14 - Tables and charts Week 15 - Angles Week 16 - Angles (continued) Week 17 - Angles (continued) Week 18 - Right, acute, and obtuse angles Week 19 - Geometric shapes Week 20 - Line of symmetry End of Year Assessment For practice with Multiple Choice questions, be sure to check out Part I of our workbook titled: 4th Grade Common Core Math: Daily Practice Workbook - Part I: Multiple Choice | 1000+ Practice Questions and Video Explanations Each question is labeled with the specific common core standard so both parents and teachers can use this workbook for their student(s). This workbook takes the Common Core State Standards and divides them up among 20 weeks. By working on these problems on a daily basis, students will be able to (1) find any deficiencies in their understanding and/or practice of math and (2) have small successes each day that will build competence and confidence in their abilities.
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Kids Summer Academy by ArgoPrep: Grade 4-5
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12 Weeks of Math, Reading, Science, Logic, Fitness and Yoga Prepare your child for Grade 5 with our award-winning Kids Summer Academy Grade 4-5 workbook. The Kids Summer Academy Series is designed to keep students engaged and prevent summer learning loss. More importantly, students are introduced to Grade 5 concepts so they can be one step ahead when they start their school year. Students will be able to review and practice English Language Arts, Mathematics, Science, Writing and more! ArgoPrep is a trusted brand used by teachers, parents and students nationwide. Kids Summer Academy series by ArgoPrep has been carefully crafted by state certified teachers and educators to provide your child with high-quality content and material to prepare for the new school year. In addition, all of our workbooks come equipped with video explanations that you can access for free on our website at This workbook includes: 12 weeks of curriculum for Grade 4-5 Prevent summer learning loss and get ready for Grade 5 Includes Reading, Math, Science, Fitness, Yoga, Logic, and Puzzles Detailed video explanations accessible on our website from anywhere Our workbook has been carefully designed and crafted by licensed teachers to give students  an incredible learning experience. Students start off the week with English activities followed by Math practice. Throughout the week, students have several fitness activities to complete. Making sure students stay active is just as important as practicing mathematics. We introduce yoga and other basic fitness activities that any student can complete. Each week includes a science experiment which sparks creativity and allows students to visually understand the concepts. On the last day of each week, students will work on a fun puzzle. ArgoPrep is one of the leading providers of supplemental educational products. Give your child the education they deserve!
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The Sieve of Eratosthenes:

By applying the divisibility rules to a hundred chart we can determine which of the numbers between 1 and 100 are prime. This method was developed many years ago by a mathematician and still today bears his name.

  1. Circle 2, because it IS a prime number.
  2. Cross out all even numbers except for two. If the number is even (and the number is not 2), the number must be composite so it is NOT prime.
  3. Circle 3. It IS prime.
  4. Cross out all other numbers divisible by three. Not sure? Add the digits together – if the sum is divisible by three then so is the number. And if the number is divisible by three it is composite and therefore NOT prime.
  5. Cross out all numbers divisible by four. You can find out if a number is divisible by four by using the divisibility rule of four. If the last two digits are divisible by four than the number is. And if the number is divisible by four it’s NOT prime.
  6. Circle 5. 5 IS a prime number.
  7. Cross out all numbers divisible by five. Is the last digit a zero or a five? If so, the number is divisible by five and is NOT prime.
  8. Cross out all numbers divisible by six. (Hint, these should all be crossed out already.) If the number is even and divisible by three it is divisible by six and therefore NOT prime.
  9. Circle 7. 7 IS prime.
  10. Cross out all numbers divisible by seven. No good trick here, but go through the last remaining numbers to check. Remember, if the number is divisible by seven it is NOT prime.
  11. Now, circle all of the remaining numbers.

On a fresh chart, color all of the crossed out numbers one color and all of the circled numbers another. Give 1 a color of its own. On our chart, we colored the prime numbers yellow and left the composite numbers white. We made 1 blue.

 

You can see that there are 25 prime numbers between 1 and 100. There are 74 composite numbers and then of course, there’s 1 which is neither prime nor composite. Did you chart match ours? Nicely done! This method of finding prime numbers is known as the Sieve of Eratosthenes and is named after a famous mathematician.

How Many Prime Numbers Are There?

As we found above, there are 25 prime numbers between 1 and 100, but that’s just the beginning. Mathematicians tell us that there are actually an infinite number of prime numbers in the universe!

Large Prime Numbers

While many prime numbers are small (2, 3, 5, etc.) some prime numbers are very large! Although calculations tell us that prime numbers are less and less likely to be prime the larger the numbers get some very large prime numbers have been discovered. In fact, the largest prime number ever discovered contains more than 20,000 digits.

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Prime Numbers in the Real World

Prime numbers are far more than just a cool math thing to know. Prime numbers are used daily by encryption specialists to secure some of the most valuable assets in the world. By multiplying two large prime numbers together, we are able to achieve an extremely large and nearly un-factorable number to be used in encryption.

Right now, prime numbers are also being used to establish the color intensity of pixels on your screen.

Prime numbers are even found in nature. Cicadas, for example, time their life cycles based on prime numbers.

The bottom line is, that whether or not you know it, you depend on prime numbers each and every day.

 

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