Factors and multiples grade 4

Factors and Multiples Grade 4

1. Factors and Multiples of a Number

2. At the end of this lesson, the learner should be able to accurately find all the factors and multiples of a given number ; correctly write a given number as a product of its factors; and correctly solve problems involving factors and multiples of a number.

3. How can you determine the factors and multiples of a given number? How can you write a given number as a product of its factors?

4. Before we start our discussion on factors and multiples, let us see if you have mastered your multiplication skills. (Click on the link to access the exercise.) “Tug Team Multiplication”. Math Playground. Retrieved 13 March 2019 from http://bit.ly/2TCMl6D

5. Did you defeat the computer in the tug-team multiplication? How did you come up with the product of the two given numbers? What are the different strategies that you can share about getting the product of two numbers? What if the given number is already a product, can you still give two possible numbers that can be multiplied to get the given number as result?

6. Factors whole numbers used to multiply together to get another number; numbers that can divide a given number equally 1 Example:

7. 2 Multiples numbers obtained by multiplying the given number by whole numbers . Example: Multiples of 4: 4, 8, 12, 16, 20, 24 … …  

8. 3 Abundant number numbers whose sum of all its factors (excluding itself) is greater than the number itself Example: Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36 .  

9. 3 Abundant number numbers whose sum of all its factors (excluding itself) is greater than the number itself Example: Factors of 36 are 1 , 2 , 3 , 4 , 6 , 9 , 12 , 18 and 36 . The sum of the factors except 36 is given by: Thus, 36 is an abundant number.  

10. 4 Deficient numbers numbers whose sum of all its factors (excluding itself) is less than the number itself Example: Factors of 21 are 1 , 3 , 7 and 21 .  

11. 4 Deficient numbers numbers whose sum of all its factors (excluding itself) is less than the number itself Example: Factors of 21 are 1 , 3 , 7 and 21 . The sum of the factors except 21 is 11. Thus, 21 is a deficient number.  

12. 5 Perfect numbers numbers whose sum of all its factors (excluding itself) is equal to the number itself Example: Factors of 28 are 1 , 2 , 4 , 7 , 14 and 28 .  

13. 5 Perfect numbers numbers whose sum of all its factors (excluding itself) is equal to the number itself Example: Factors of 28 are 1, 2, 4, 7, 14 and 28 . The sum of the factors except 28 is 28. Therefore, 28 is a perfect number.  

14. Example 1 : Find all the factors of 26.

15. Example 1 : Find all the factors of 26. Solution : List down all possible pairs that when multiplied together will give a product of 26. Since all numbers are divisible by 1, then the first pair is:  

16. Example 1 : Find all the factors of 26. Solution : List down all possible pairs that when multiplied together will give a product of 26. If the number is even, then we can say that one of its factors is 2. Thus, the next pair is:  

17. Example 1 : Find all the factors of 26. Solution : List down all possible pairs that when multiplied together will give a product of 26. As we increase one of the factors, the other factors tend to decrease. Then, check if there is a number between 2 and 13 that can divide 26 equally.

18. Example 1 : Find all the factors of 26. Solution : As we increase one of the factors, the other factors tends to decrease. Then, check if there is a number between 2 and 13 that can divide 26 equally. Since there are no numbers between 2 and 13 that can divide 26 equally, the list is already completed.

19. Example 1 : Find all the factors of 26. Solution : List down all possible pairs that when multiplied together will give a product of 26. Summarize the list of factors. Thus, the factors of 26 are 1, 2, 13 and 26  

20. Example 2 : Find the first five multiples of 3 .

21. Example 2 : Find the first five multiples of 3 . Solution : List down the first five whole numbers to be multiplied by 3. Therefore, the first five multiples of 3 are 3, 6, 9, 12 and 15 .  

22. Individual Practice: What is the smallest and the largest factors of any number? Which of the following numbers are abundant, deficient and perfect: 16, 13, 6 ?

23. Group Practice : To be done in groups of 4. Mr. Lopez has an activity for his Science class. He has 48 students in his class and he wants to have not less than 4 members but not more than 10 members per group. In how many ways can he group the class with equal number of members?

24. Factors whole numbers used to multiply together to get another number; numbers that can divide a given number equally 1 2 3 Multiples numbers obtained by multiplying the given number by whole numbers. 3 Abundant Numbers numbers whose sum of all its factors (excluding itself) is greater than the number itself

25. Deficient Numbers numbers whose sum of all its factors (excluding itself) is less than the number itself 4 5 Perfect Numbers numbers whose sum of all its factors (excluding itself) is equal to the number itself.

26. How do you determine the factors and multiples of a given number? Why do we need to learn about identifying the factors and multiples of a number? Now that you have learned how to identify factors and multiples of a number, are you ready to use them in finding prime and composite numbers ?