GCF of 4 and 5 is the largest possible number that divides 4 and 5 exactly without any remainder. The factors of 4 and 5 are 1, 2, 4 and 1, 5 respectively. There are 3 commonly used methods to find the GCF of 4 and 5 - prime factorization, Euclidean algorithm, and long division.
| 1. | GCF of 4 and 5 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 4 and 5?
Answer: GCF of 4 and 5 is 1.
Explanation:
The GCF of two non-zero integers, x(4) and y(5), is the greatest positive integer m(1) that divides both x(4) and y(5) without any remainder.
Methods to Find GCF of 4 and 5
The methods to find the GCF of 4 and 5 are explained below.
- Long Division Method
- Using Euclid's Algorithm
- Prime Factorization Method
GCF of 4 and 5 by Long Division
GCF of 4 and 5 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 5 (larger number) by 4 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (4) by the remainder (1).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (1) is the GCF of 4 and 5.
GCF of 4 and 5 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 = 5 and Y = 4
- GCF(5, 4) = GCF(4, 5 mod 4) = GCF(4, 1)
- GCF(4, 1) = GCF(1, 4 mod 1) = GCF(1, 0)
- GCF(1, 0) = 1 (∵ GCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of GCF of 4 and 5 is 1.
GCF of 4 and 5 by Prime Factorization
Prime factorization of 4 and 5 is (2 × 2) and (5) respectively. As visible, there are no common prime factors between 4 and 5, i.e. they are co-prime. Hence, the GCF of 4 and 5 will be 1.
☛ Also Check:
- GCF of 4 and 18 = 2
- GCF of 4 and 10 = 2
- GCF of 25 and 30 = 5
- GCF of 4 and 12 = 4
- GCF of 90 and 135 = 45
- GCF of 36 and 96 = 12
- GCF of 2 and 8 = 2
GCF of 4 and 5 Examples
Example 1: Find the greatest number that divides 4 and 5 exactly.
Solution:
The greatest number that divides 4 and 5 exactly is their greatest common factor, i.e. GCF of 4 and 5.
⇒ Factors of 4 and 5:- Factors of 4 = 1, 2, 4
- Factors of 5 = 1, 5
Therefore, the GCF of 4 and 5 is 1.
Example 2: For two numbers, GCF = 1 and LCM = 20. If one number is 5, find the other number.
Solution:
Given: GCF (z, 5) = 1 and LCM (z, 5) = 20
∵ GCF × LCM = 5 × (z)
⇒ z = (GCF × LCM)/5
⇒ z = (1 × 20)/5
⇒ z = 4
Therefore, the other number is 4.Example 3: Find the GCF of 4 and 5, if their LCM is 20.
Solution:
∵ LCM × GCF = 4 × 5
⇒ GCF(4, 5) = (4 × 5)/20 = 1
Therefore, the greatest common factor of 4 and 5 is 1.
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FAQs on GCF of 4 and 5
What is the GCF of 4 and 5?
The GCF of 4 and 5 is 1. To calculate the GCF of 4 and 5, we need to factor each number (factors of 4 = 1, 2, 4; factors of 5 = 1, 5) and choose the greatest factor that exactly divides both 4 and 5, i.e., 1.
If the GCF of 5 and 4 is 1, Find its LCM.
GCF(5, 4) × LCM(5, 4) = 5 × 4
Since the GCF of 5 and 4 = 1
⇒ 1 × LCM(5, 4) = 20
Therefore, LCM = 20
☛ Greatest Common Factor Calculator
What is the Relation Between LCM and GCF of 4, 5?
The following equation can be used to express the relation between Least Common Multiple and GCF of 4 and 5, i.e. GCF × LCM = 4 × 5.
How to Find the GCF of 4 and 5 by Prime Factorization?
To find the GCF of 4 and 5, we will find the prime factorization of the given numbers, i.e. 4 = 2 × 2; 5 = 5.
⇒ There is no common prime factor for 4 and 5. Hence, GCF (4, 5) = 1.
☛ What are Prime Numbers?
How to Find the GCF of 4 and 5 by Long Division Method?
To find the GCF of 4, 5 using long division method, 5 is divided by 4. The corresponding divisor (1) when remainder equals 0 is taken as GCF.
What are the Methods to Find GCF of 4 and 5?
There are three commonly used methods to find the GCF of 4 and 5.
- By Long Division
- By Prime Factorization
- By Euclidean Algorithm
