Math 5 DLP 9 - Finding The Greatest Common Factor Of Two .

5Module 9MATHFinding the Greatest Common Factor of Twoor More NumbersA DepEd-BEAM Distance Learning Program supported by the Australian Agency for International Development

To the LearnerHello dear learner. Did you enjoy solving the problem in theprevious lesson? I hope you have familiarized and mastered alreadythe steps in solving word problems. Today you are going to learn howto find the greatest common factor of two or more numbers.Let’s Learn ThisThis module covers the lesson on finding the greatest commonfactor of two or more numbers. The knowledge and skills that you willgain from the activities will be very useful inputs in the cominglessons, that you are going to learn.As you go through this module, you should be able to:¾give the common factors of a given numbers¾find the greatest common factor of given numbers¾complete the greatest common factor of given using any ofthe methods being introduced.Let’s Try ThisA. Copy the Greatest Common Factor.1.) 5 1x 510 2 x 5GCF 2.) 6 2 x 39 3x3GCF 4.) 12 3 x2 x15 3 x5GCF 5.) 3 3 x 19 3x312 3 x 2 x 2GCF - 53 -3.)6 2x38 2x2x2GCF

B. Find the factors and the common factors of each pair ofnumbers. Then encircle the Greatest Common Factor.(Number 6 is done for you.)Number6.) 812FactorsCommon Facors1,2,4,81 , 2 ,3, 4 , 6 121,2,47.) 18458.) 24329.) 202510.) 2142Let’s Study ThisWord Problem:Mr. Cejas plans to organize the Math club of 16 boys and 20girls what is the biggest number of members each group can havewhich would have an equal number of boys and girls?To get the answer, find the Greatest Common Factor of 16and 20.Method 1. List all the factor of 16 and 20Get the CommonFactor16 : 1 , 2 , 4 , 8 , 1620 : 1 , 2 , 4 , 5 , 10 , 20 16 : 1 , 2 , 420 : 1 , 2 , 4Select the GreatestCommon FactorGCF 4Method 2. Use Prime FactorizationBy Factor Tree20164x 44 x52x2x2x22x2 x 5Find the CommonPrime Factors16: 2 x 220: 2 x 2- 54 -Find the Product16: 2 x 2 420: 2 x 2 4GCF 4

Method 3. By Continuous Division Write the number horizontally16 20 Think of prime numbers that 16 and 20 can divide. (2)2 16 20 Divide the given numbers by the given prime numbers.Write the quotient below the dividends.2 16 208 10 Continue the process until none of the numbers have acommon divisor except 1.2 16 2028 10454 and have no common factor except 1.Stop here.GCF 2 x x 4Therefore; the greatest number of number in each group is 4.Another Example:1. What is the GCF of 12 and 18?Find the CommonPrime factors andfind the productBy Factor Tree18124 x 32x2 x 32 x912: 2 x 3 618: 2 x 3 62 x 3x3GCF 6Therefore, the GCF of 12 and 18 is 6.2. What is the GCF of 36, 54 72?By Continuous Division2 36 54 723318 27 36629 123 42, 3 and 4 has nocommon factor except 1.GCF 2 x 3 x 3 18Therefore, GCF of 36, 54 and 72 is 18.- 55 -

Let’s Do ThisA. Give all the factors of each number. Then copy the greatestcommon factor. First number is done for you.1.)6: 1 , 2 , 3 , 615: 1 , 3 ,5 , 152.)GCF . 3 .4.)12:16:3.) 14:21:GCF:GCF:5.) 12:18:24:GCF:16:48:GCF:B. Find the GCF of each pair of numbers as a product of primefactors. Number 1 is done for you.6.) 18 2 x 3 x 327 3 x 3 x 3GCF 3 x 3 97.) 12 30 GCF 9.) 36 54 GCF 8.) 14 35 GCF 10.) 243036GCF Let’s Do MoreA. Use the continuous division method to find GCF.1.) 36 , 63GCF 2.) 24 , 96GCF 4.) 72 , 108GCF 3.) 30 , 105GCF 5.) 24 , 48 , 60GCF - 56 -

Let’s Remember ThisThe Greatest Common Factor (GCF) of two or more numbersis the largest number that is a factor of all the given numbers. It isless than the numbers or equal to one of the numbers. If the GCFof the given numbers is 1 then the numbers are said to berelatively prime.The methods for finding the GCF of numbers are theList Down Method, Prime Factorization Method andContinuous Division.Let’s Test OurselvesA. Give all the factors of each number. Then find the GCF.1.) 21 35 GCF 2.) 25 40 GCF 3.) 30 45 GCF B. Express each number as a product of its prime factors then findthe GCF.4.) 21 27 GCF 5.) 18 45 GCF 6.) 24 20 40 GCF C. Find the GCF of each set of number using continuous division.7.) 36 , 45GCF 8.) 42 , 63GCF 10.) 12 , 36 and 120GCF - 57 -9.) 30 , 105GCF

Let’s Enrich OurselvesAdditional Exercise:A. Fill in the box with the correct answer.1.)2.) 2 24 7218 2163GCF 23.) 5 20 30 4036484232 61 3GCF GCF 4.) 2 36 60 108182 65410185B.Use the factor tree to find the GCF.5.) 63 , 72GCF 6.) 40 , 105GCF Let’s Consider ThisIf your score is above 7, then proceed to the next module.If you got 5-6 then answer another exercise.If you got below 5, review the whole module.- 58 -

Answer KeyLet’s Try This1.2.3.4.5.6.532331,2,47. 1 , 3 ,98. 1 , 2, 4 ,9. 1 ,Let’s Test Ourselves1.)2.)3.)4.)5.)6.)7.)8.)9.)10.)85Let’s Do More10. 1 , 3 , 7 , 211.)2.)3.)4.)5.)Let’s Do ’s Enrich OurselvesA.B.5.)9751539492115126.) 5- 59 -924153612

The Greatest Common Factor (GCF) of two or more numbers is the largest number that is a factor of all the given numbers. It is less than the numbers or equal to one of the numbers. If the GCF of the given numbers is 1 then the numbers are said to be relatively prime.