GRADE FIVE MATHEMATICS
Hello Boys and Girls! Were you able to challenge yourself at school last week? If so, I hope you had an exciting challenge. This week we will examine Prime and Composite numbers. In addition, we will do prime factorization of numbers, but first let us check last week’s answers.
Answers for last week. Factors of 6 are 1,2,3,6. Factors of 8 are 1,2,4,8. Factors of 11 are 1 and 11. Factors of 16 are 1,2,4,8, 16. Factors of 10 are 1, 2, 5, 10. Factors of 12 are 1, 2, 3, 4, 6,12. Factors of 9 are 1,3,9. Factors of 15 are 1,2,5,15. Factors of 18 are 1,2,3,6,9,18. Factors of 20 are 1,2,4,5, 10,20. Factors of 24 are 1,2,3,4,6,8,12,24. Factors of 28 are 1,2,4,7,14,28. Factors of 30 are 1,2,3,5,6,10,15,30. Factors of 32 are 1,2,4,8,16,32. Factors of 36 are 1,2,3,4,6,9,12,18,36.
Prime and Composite Numbers A prime number is one that has only itself and 1 as factors. e.g. 2,3,5,7,11
Steps to find Prime Numbers 1. Get a number chart with the numbers 1 to 200 or write down 1 to 200. 2. Cross off all the multiples of two that are greater than 2. 3. Cross off all the multiples of 3 that are greater than 3. 4. Cross of all the multiples of 5 that are greater than 5. 5. Cross off all the multiples of 7 starting with 14. 6. Cross off all the multiples of 11. 7. Cross off all the multiples of 13. 8. Look at what’s left. When completed, all that should be left are prime numbers and 1. 9. All the numbers crossed off are composite numbers because they have more than 1 factor pair. A prime number has only one factor pair, 1 and itself. I hope that you were able to find all the prime and composite numbers. Let us now complete activities that would help us to masterthe concept.
Practice Exercise 1. Write down all the prime numbers between 2 and 100. 2. Write down all the composite numbers from 1 to 60.
Look at the numbers below and state which of these numbers are prime and which are composite. 1. 12 2. 13 3. 17 4. 18 5. 19 6. 24 7. 25 8. 29 9. 33 10. 37 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 41 43 49 51 57 60 63 67 73 77
Factorisation Last week, we also examined the Factor Tree method. When we create factor trees we are able to determine the prime factors of numbers. Do you remember the diagram below?
When creating a factor tree, we factorise all the numbers given until we arrive at the prime factors. Therefore the prime factorization of 12 is 2x2x3. Observe that 4 is a factor of 12 but it is not a prime number.
Remember: The prime factors of any given numbers are its factors that are prime numbers.
Let us now use the Factor Tree Method to write the prime factorization of the following. 1 8 2 10 3 15 4 16 5 20 6 24 7 28 8 60 9 72 10 96
Common Factors When we find the factors of two or more numbers, and then find some factors are the same (“common”), then they are the “common factors”.
Example: 12 and 16 • The factors of 12 are: 1, 2, 3, 4, 6 and 12 • The factors of 16 are: 1, 2, 4, 8 and 16 So the common factors of 12 and 16 are: 1, 2 and 4
Now, write the common factors of the following: 1. 6 and 9 2. 6 and 8 3. 12 and 16 4. 9 and 12 5. 8 and 20 6. 18 and 30 7. 25 and 40 8. 15 and 20 9. 24 and 42 10. and 48
Can you remember the concept of reducing fractions to lowest terms? You did that in Grade 5. We can use common factors to simplify fractions or reduce them to lowest terms. For example: 12 = 6 = 3 16 8 4 In this case, we divided by the common factor 2 and we completed the task in two stages. We could have completed the task in one stage by dividing by 4.