Republic of the Philippines
Autonomous Region in Muslim Mindanao
RC-AL KHWARIZMI INTERNATIONAL COLLEGE FOUNDATION, INC.
Department of Liberal Arts
National Highway, Basak Malutlut, Marawi City
LAS #6 Date: _____________________________
Course Number: Math 1 Course Title: Fundamentals of Mathematics
Topic Title: Greatest Common Factor (GCF)
Objective: Identify the greatest common factor of a given set of numbers through four methods.
Activity Title: Identify the greatest common factor of a given set of numbers through four
methods.
Reference: Beyond Math By Loly Ong, Angelyn R. Lao, Maria Jenny Tan, & Judy W. Sy
CONCEPT NOTES
The Greatest Common Factor (GCF) is the largest common factor of two or more
numbers.
Here are four methods used in finding the GCF of a set of numbers.
I. Listing Method
Steps:
1. List down all the factors of the given numbers and group them by sets enclosed by {}.
2. List down another set containing the common factors of the sets created in step 1.
3. Among the numbers listed in the set of step 2, the GCF is the number in that set with
the greatest value.
Example 1: Find the greatest common factor of 36 and 54.
Solution: Let 𝐴 = set of factors of 36
= {1, 2, 3, 4, 6, 9, 12, 18, 36}
Let 𝐵 = set of factors of 54
= {1, 2, 3, 6, 9, 18, 27, 54}
Common factors of set 𝐴 and set 𝐵 are contained in the set {1, 2, 3, 6, 9, 18}
Since 18 is the greatest value of the set, hence GCF(36,54)=18.
II. Prime Factorization
Steps:
1. Represent the given numbers as products of their prime factors.
2. Choose the common prime factors of all the given numbers.
3. The product of the common prime factors is the GCF.
Example 2: Find the greatest common factor of 36 and 54.
Solution:
Step 1: 54 = 2 × 33
36 = 22 × 32 .
Step 2: Common prime factors of 54 and 36 are 2, 3, and 3.
Step 3: GCF(54,36) = 32 × 2 = 18.
Check: 54 ÷ 18 = 3,
36 ÷ 18 = 2,
Therefore, 18 is the GCF because 2 and 3 have no common factor other than 1.
III. Continuous Division Method
Steps:
1. Arrange the numbers horizontally.
2. Find a prime number that will divide all the given numbers.
3. Write the quotient below each given number.
4. Repeat step 2 and step 3 until step cannot be satisfied.
5. GCF is the product of all prime divisors.
Example 3: Find the greatest common factor of 36 and 54.
“There’s always future in Mathematics.” Page 1
Solution:
2 36 54
3 18 27
3 6 9
2 3
This is the last step since step 2 can no longer be used.
Hence, GCF(36,54) = 2 × 3 × 3 = 18.
IV. Euclidean Algorithm
Steps:
1. Divide the larger number by the smaller number.
2. Divide the previous divisor by the previous remainder.
3. Continue step 2 until the remainder is equal to zero.
4. GCF is the last divisor that gives a zero remainder.
This algorithm was discovered by Euclid in 300 B.C. This method is useful when
dealing with large numbers and in computer programming.
Example 4: Find the GCF of 3 144 and 1 539.
Solution: 2
Step 1: 1 539√3 144
−3 078
66
Steps 2 and 3:
23 3 7
66√1 539 21√66 3√21
− 132 − 63 − 21
219 3 0
− 198
21
Step 4: Therefore, GCF(3 144,1 539) = 3.
Take Note: We can also find the GCF of three or more numbers using a method stated
above.
MASTERY PRACTICE :Find the GCF of 84 and 96 using the following methods. Show all your
solution.
1. Listing Method 3. Prime Factorization
2. Continuous Division Method 4. Euclidean Algorithm
CHECK FOR UNDERSTANDING/ASSIGNMENT
Instruction: Find the GCF of 405, 370, and 590 using the following methods. Show all your
solution.
1. Listing Method 3. Prime Factorization
2. Continuous Division Method 4. Euclidean Algorithm
“There’s always future in Mathematics.” Page 2
