In Mathematics, the Greatest Common Factor of two or more numbers is the greatest positive integer x, which divides both the given numbers. The Greatest Common Factor is additionally referred to as GCF. In this Greatest can be replaced with highest, and factor can be replaced with Divisor. So GCF is also known as HCF (Highest Common Factor), Greatest Common Divisor (GCD), and Highest Common Divisor (HCD).
On this page for better understanding, we will provide various questions with a quick explanation here. In this article, we have covered different questions on Greatest Common Factor (GCF) for enhancing their skills as well as better practice. GCF is used most of the time with fractions, which are used a great deal in everyday lifestyle.
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Examples of finding Greatest Common Factor(GCF)
Problem 1:Â
Find the GCF of 72 and 81.
Solution:
Given the values are 72, and 81.
Now, we will the factors.
So, the factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18.
Factors of 81 are 1, 3, 9, 27.
So, the common factors of 72, 81 are 1, 3, 9.
Next, write the Greatest Common Factor among them is 9.
Thus, the Greatest Factor of the given numbers is 9.
Problem 2:Â
What is the Greatest Common Factor (GCF) of 11, 121, 143?
Solution:
As given in the question, the values are 11, 121, 143.
Now, will find the greatest common factor. So, first, write the common factors.
The factors of 11 are 1, 11
The factors of 121 are 1, 11
The factors of 143 are 1, 11,
The common factors of 11, 121, 143 are 1, 11.
Therefore, the Greatest Common factor among them is 11.
Problem 3:
Let us write the Greatest Factor of 15 and 35.
Solution:
Given the values,
First, we have to list the factors of 15 and 35 and then find out the common factors.
Now, write the factors of 15 are 1, 3, 5, and 15.
The factors of 35 are 1, 5, 7.
The common factors of 15 and 35 are 1, 5.
Among these numbers, 5 is the greatest (largest) number.
Thus, the GCF of 15 and 35 is 5. This is written as GCF(15, 35) = 5.
Problem 4:
What is the GCF of 26, 62?
Solution:
Given the values, 26 and 62.
Now, write the factors.
The factors of 26 are 1, 2, 13.
The factors of 62 are 1, 2.
So, the common factors are 1, 2.
Among them, the Greatest (largest) factor is 2.
Therefore, the Greatest Common Factor of 26 and 62 is 2.
Problem 5:
Find the GCF (Greatest Common Factor) of 48, 148, and 36 using the prime factorization.
Solution:
Given the values for finding GCF is 48, 148, and 36.
Using Prime Factorization, now write the factors.
So, the factors of 48 are 2 x 2 x 2 x 6.
Factors of 148 are 2 x 2 x 37.
The factors of 36 are 2 x 2 x 3 x 3.
The common factors are 2 x 2 = 4
Thus, the GCF of given numbers is 4.
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Problem 6:
What is the greatest common factor of 45,120?
Solution:
Given the values are 45, 120.
Now, we have to write the factors of 45 are 1, 3, 5, 9, 15.
The Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15.
Therefore, the common factors of 45 and 120 are 1, 3, 5, and 15.
Hence, the Greatest Common divisor (GCD) or GCF of the given numbers is 15.
Problem 7:Â
Write the Greatest Common Factors of 77, 99, 121?
Solution:
Given the values 77, 99, and 121.
First, write the common factor.
The factors of 77 are 1, 7, and 11.
The factors of 99 are 1, 3, 11.
The factors of 121 are 1, 11
Therefore, the common factors are 1, 11.
So, the Greatest Common Factor (GCF) of 77, 99, and 121 is 11.
Problem 8:Â
Two pipes are 32m and 36m long. The pipes are to be cut into pieces of equal length. Find each piece’s maximum length of pipe.
Solution:
As given in the question,
Two pipes length is 32m and 36m.
GCF is the required length of each piece of pipe.
32 = 2 x 16
36 = 2 x 28
The common greatest factor is 2.
Hence, the required pipe maximum length of each piece is 2m.
Problem 9:
Find the greatest common divisor (GCD) of 128 and 96.
Solution:
Given the values,
By Using the method of prime factorisation,
The factors of 128 are 2 x 2 x 2 x 2 x 2 x 2 x 2
The factors of 96 are 2 x 2 x 2 x 2 x 2 x 3
Now, write the Common factors of GCF (128, 96) = 2 x 2 x 2 x 2 x2 = 32.
Thus, the GCF is 32.
(OR)
By Euclid’s division algorithm,
128 = 96 x 1 + 32
96 = 32 x 3 + 0
Hence, the Greatest Common Factor (GCF) of 128 and 96 is 32.
Problem 10:
What is the GCF of 19 and 17?
Solution:
Given the values,
First, we have to list the factors of 19 and 17 and then find out the common factors.
The factors of 19 are 1, and 19.
The factors of 17 are 1, and 17.
The common factors of seven and 17 are 1.
Among these numbers, 1 is the greatest (largest) number.
Thus, the GCF of 19 and 17 is 1. This is written as GCF(19, 17) = 1.Â
FAQ’s on Examples of GCF
1. Write the difference between the HCF and GCF?
The HCF and GCF both are the same. There is no difference between HCF and GCD. Greatest Common Factor (GCF), Greatest Common Measure (GCM), and Highest Common Divisor all are similar.
2. Is GCF and LCM both are the same?
LCM stands for Least Common Multiple. LCM of two numbers is the smaller value that is divisible by both two numbers. Whereas GCF is the highest common factor of two numbers, which can divide the two numbers evenly. Therefore, LCM and GCD are different.
3. Is GCD and HCF the same?
GCD is that the Greatest common divisor and HCF are that the Highest Common Factor. Both are the same.
4. What are the Applications of Greatest Common Factor (GCF)?
The concept of the greatest divisor or the highest common factor is employed in many real-life incidents. Other applications like arranging students in rows and columns in equal numbers, diving a group of people into smaller sections, and etc.,