GCF of 4 and 20
GCF of 4 and 20 is the largest possible number that divides 4 and 20 exactly without any remainder. The factors of 4 and 20 are 1, 2, 4 and 1, 2, 4, 5, 10, 20 respectively. There are 3 commonly used methods to find the GCF of 4 and 20 - Euclidean algorithm, long division, and prime factorization.
1. | GCF of 4 and 20 |
2. | List of Methods |
3. | Solved Examples |
4. | FAQs |
What is GCF of 4 and 20?
Answer: GCF of 4 and 20 is 4.
Explanation:
The GCF of two non-zero integers, x(4) and y(20), is the greatest positive integer m(4) that divides both x(4) and y(20) without any remainder.
Methods to Find GCF of 4 and 20
Let's look at the different methods for finding the GCF of 4 and 20.
- Using Euclid's Algorithm
- Long Division Method
- Listing Common Factors
GCF of 4 and 20 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 = 20 and Y = 4
- GCF(20, 4) = GCF(4, 20 mod 4) = GCF(4, 0)
- GCF(4, 0) = 4 (∵ GCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of GCF of 4 and 20 is 4.
GCF of 4 and 20 by Long Division
GCF of 4 and 20 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 20 (larger number) by 4 (smaller number).
- Step 2: Since the remainder = 0, the divisor (4) is the GCF of 4 and 20.
The corresponding divisor (4) is the GCF of 4 and 20.
GCF of 4 and 20 by Listing Common Factors
- Factors of 4: 1, 2, 4
- Factors of 20: 1, 2, 4, 5, 10, 20
There are 3 common factors of 4 and 20, that are 1, 2, and 4. Therefore, the greatest common factor of 4 and 20 is 4.
☛ Also Check:
- GCF of 72 and 84 = 12
- GCF of 15 and 75 = 15
- GCF of 12 and 56 = 4
- GCF of 60 and 72 = 12
- GCF of 28 and 40 = 4
- GCF of 16 and 25 = 1
- GCF of 16 and 48 = 16
GCF of 4 and 20 Examples
-
Example 1: Find the GCF of 4 and 20, if their LCM is 20.
Solution:
∵ LCM × GCF = 4 × 20
⇒ GCF(4, 20) = (4 × 20)/20 = 4
Therefore, the greatest common factor of 4 and 20 is 4. -
Example 2: The product of two numbers is 80. If their GCF is 4, what is their LCM?
Solution:
Given: GCF = 4 and product of numbers = 80
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 80/4
Therefore, the LCM is 20. -
Example 3: For two numbers, GCF = 4 and LCM = 20. If one number is 4, find the other number.
Solution:
Given: GCF (z, 4) = 4 and LCM (z, 4) = 20
∵ GCF × LCM = 4 × (z)
⇒ z = (GCF × LCM)/4
⇒ z = (4 × 20)/4
⇒ z = 20
Therefore, the other number is 20.
FAQs on GCF of 4 and 20
What is the GCF of 4 and 20?
The GCF of 4 and 20 is 4. To calculate the GCF (Greatest Common Factor) of 4 and 20, we need to factor each number (factors of 4 = 1, 2, 4; factors of 20 = 1, 2, 4, 5, 10, 20) and choose the greatest factor that exactly divides both 4 and 20, i.e., 4.
How to Find the GCF of 4 and 20 by Long Division Method?
To find the GCF of 4, 20 using long division method, 20 is divided by 4. The corresponding divisor (4) when remainder equals 0 is taken as GCF.
How to Find the GCF of 4 and 20 by Prime Factorization?
To find the GCF of 4 and 20, we will find the prime factorization of the given numbers, i.e. 4 = 2 × 2; 20 = 2 × 2 × 5.
⇒ Since 2, 2 are common terms in the prime factorization of 4 and 20. Hence, GCF(4, 20) = 2 × 2 = 4
☛ Prime Number
What are the Methods to Find GCF of 4 and 20?
There are three commonly used methods to find the GCF of 4 and 20.
- By Long Division
- By Listing Common Factors
- By Prime Factorization
What is the Relation Between LCM and GCF of 4, 20?
The following equation can be used to express the relation between Least Common Multiple and GCF of 4 and 20, i.e. GCF × LCM = 4 × 20.
If the GCF of 20 and 4 is 4, Find its LCM.
GCF(20, 4) × LCM(20, 4) = 20 × 4
Since the GCF of 20 and 4 = 4
⇒ 4 × LCM(20, 4) = 80
Therefore, LCM = 20
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