GCF of 5 and 6 is the largest possible number that divides 5 and 6 exactly without any remainder. The factors of 5 and 6 are 1, 5 and 1, 2, 3, 6 respectively. There are 3 commonly used methods to find the GCF of 5 and 6 - long division, prime factorization, and Euclidean algorithm.
| 1. | GCF of 5 and 6 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 5 and 6?
Answer: GCF of 5 and 6 is 1.
Explanation:
The GCF of two non-zero integers, x(5) and y(6), is the greatest positive integer m(1) that divides both x(5) and y(6) without any remainder.
Methods to Find GCF of 5 and 6
The methods to find the GCF of 5 and 6 are explained below.
- Prime Factorization Method
- Using Euclid's Algorithm
- Long Division Method
GCF of 5 and 6 by Prime Factorization
Prime factorization of 5 and 6 is (5) and (2 × 3) respectively. As visible, there are no common prime factors between 5 and 6, i.e. they are coprime. Hence, the GCF of 5 and 6 will be 1.
GCF of 5 and 6 by Euclidean Algorithm
As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.
Here X = 6 and Y = 5
- GCF(6, 5) = GCF(5, 6 mod 5) = GCF(5, 1)
- GCF(5, 1) = GCF(1, 5 mod 1) = GCF(1, 0)
- GCF(1, 0) = 1 (∵ GCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of GCF of 5 and 6 is 1.
GCF of 5 and 6 by Long Division
GCF of 5 and 6 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 6 (larger number) by 5 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (5) by the remainder (1).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (1) is the GCF of 5 and 6.
☛ Also Check:
- GCF of 30 and 40 = 10
- GCF of 25 and 45 = 5
- GCF of 92 and 23 = 23
- GCF of 10 and 20 = 10
- GCF of 16 and 20 = 4
- GCF of 18 and 28 = 2
- GCF of 4 and 18 = 2
GCF of 5 and 6 Examples
Example 1: The product of two numbers is 30. If their GCF is 1, what is their LCM?
Solution:
Given: GCF = 1 and product of numbers = 30
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 30/1
Therefore, the LCM is 30.See AlsoValue categoriesExample 2: For two numbers, GCF = 1 and LCM = 30. If one number is 6, find the other number.
Solution:
Given: GCF (z, 6) = 1 and LCM (z, 6) = 30
∵ GCF × LCM = 6 × (z)
⇒ z = (GCF × LCM)/6
⇒ z = (1 × 30)/6
⇒ z = 5
Therefore, the other number is 5.Example 3: Find the greatest number that divides 5 and 6 exactly.
Solution:
The greatest number that divides 5 and 6 exactly is their greatest common factor, i.e. GCF of 5 and 6.
⇒ Factors of 5 and 6:- Factors of 5 = 1, 5
- Factors of 6 = 1, 2, 3, 6
Therefore, the GCF of 5 and 6 is 1.
Show Solution >
go to slidego to slidego to slide
Ready to see the world through math’s eyes?
Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.
Book a Free Trial Class
FAQs on GCF of 5 and 6
What is the GCF of 5 and 6?
The GCF of 5 and 6 is 1. To calculate the greatest common factor (GCF) of 5 and 6, we need to factor each number (factors of 5 = 1, 5; factors of 6 = 1, 2, 3, 6) and choose the greatest factor that exactly divides both 5 and 6, i.e., 1.
How to Find the GCF of 5 and 6 by Long Division Method?
To find the GCF of 5, 6 using long division method, 6 is divided by 5. The corresponding divisor (1) when remainder equals 0 is taken as GCF.
If the GCF of 6 and 5 is 1, Find its LCM.
GCF(6, 5) × LCM(6, 5) = 6 × 5
Since the GCF of 6 and 5 = 1
⇒ 1 × LCM(6, 5) = 30
Therefore, LCM = 30
☛ Greatest Common Factor Calculator
How to Find the GCF of 5 and 6 by Prime Factorization?
To find the GCF of 5 and 6, we will find the prime factorization of the given numbers, i.e. 5 = 5; 6 = 2 × 3.
⇒ There is no common prime factor for 5 and 6. Hence, GCF (5, 6) = 1.
☛ Prime Number
What are the Methods to Find GCF of 5 and 6?
There are three commonly used methods to find the GCF of 5 and 6.
- By Long Division
- By Prime Factorization
- By Euclidean Algorithm
What is the Relation Between LCM and GCF of 5, 6?
The following equation can be used to express the relation between Least Common Multiple and GCF of 5 and 6, i.e. GCF × LCM = 5 × 6.
