GREATEST COMMON FACTOR
Definition Of Greatest Common Factor
Greatest common factor is the greatest number that is a factor of each of two or more given numbers.
More About Greatest Common Factor
Greatest Common Factor is abbreviated as G.C.F
Greatest common factor of two or more numbers can be found by successive division method and factorization method
Examples of Greatest Common Factor:
The greatest common factor of 24 and 15 is 3
The greatest common factor of 40, 50, and 25 is 5
Video Examples: Greatest Common Factor - GCF
Solved Examples on Greatest Common Factor
Ques: Which is the greatest common factor of 20 and 36?
Choices:
A. 20
B. 4
C. 36
D. 180
Correct Answer: B
Solution:
Step 1: The factors of 20 are 1, 2, 4, 5, 10, 20
Step 2: The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
Step 3: The common factors of 20 and 36 are: 1, 2, 4
Step 4: So, the greatest common factor or G.C.F. of 20 and 36 is 4
Ques: What is the G.C.F. of 45 and 75?
Choices:
A. 5
B. 10
C. 15
D. 20
Correct Answer: C
Solution:
Step 1: Divide the larger number 75 by 45. The remainder will be 30
Step 2: Divide 45 with the remainder 30. This time, the remainder is 15.
Step 3: Finally, divide 30 with the remainder 15. The remainder is 0.
Step 4: Therefore, the G.C.F. of 45 and 75 is 15
Quick Summary
- GCF is the largest factor shared by two or more numbers.
- It can be found using successive division or factorization.
- GCF is also abbreviated as G.C.F.
🍎 Teacher Insights
Use visual aids like factor trees or Venn diagrams to help students understand the concept. Start with smaller numbers and gradually increase the complexity. Emphasize the real-world applications of GCF, such as simplifying fractions.🎓 Prerequisites
- Factors
- Multiples
- Divisibility
Check Your Knowledge
Q1: What is the greatest common factor of 12 and 18?
Q2: What is the G.C.F. of 45 and 75?
Frequently Asked Questions
Q: How do I find the GCF of more than two numbers?
A: You can use the same methods (factorization or successive division), extending them to include all the numbers. Find the factors common to all the numbers and select the greatest one.
Q: What is the GCF of two prime numbers?
A: The GCF of two different prime numbers is always 1, since prime numbers only have 1 and themselves as factors.