GCF of 12 and 20 is the largest possible number that divides 12 and 20 exactly without any remainder. The factors of 12 and 20 are 1, 2, 3, 4, 6, 12 and 1, 2, 4, 5, 10, 20 respectively. There are 3 commonly used methods to find the GCF of 12 and 20 - prime factorization, long division, and Euclidean algorithm.
| 1. | GCF of 12 and 20 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 12 and 20?
Answer: GCF of 12 and 20 is 4.
Explanation:
The GCF of two non-zero integers, x(12) and y(20), is the greatest positive integer m(4) that divides both x(12) and y(20) without any remainder.
Methods to Find GCF of 12 and 20
The methods to find the GCF of 12 and 20 are explained below.
- Using Euclid's Algorithm
- Long Division Method
- Prime Factorization Method
GCF of 12 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 = 12
- GCF(20, 12) = GCF(12, 20 mod 12) = GCF(12, 8)
- GCF(12, 8) = GCF(8, 12 mod 8) = GCF(8, 4)
- GCF(8, 4) = GCF(4, 8 mod 4) = GCF(4, 0)
- GCF(4, 0) = 4 (∵ GCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of GCF of 12 and 20 is 4.
GCF of 12 and 20 by Long Division
GCF of 12 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 12 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (12) by the remainder (8).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (4) is the GCF of 12 and 20.
GCF of 12 and 20 by Prime Factorization
Prime factorization of 12 and 20 is (2 × 2 × 3) and (2 × 2 × 5) respectively. As visible, 12 and 20 have common prime factors. Hence, the GCF of 12 and 20 is 2 × 2 = 4.
☛ Also Check:
- GCF of 15 and 25 = 5
- GCF of 72 and 96 = 24
- GCF of 105 and 90 = 15
- GCF of 12 and 24 = 12
- GCF of 6 and 21 = 3
- GCF of 9 and 15 = 3
- GCF of 72 and 90 = 18
GCF of 12 and 20 Examples
Example 1: For two numbers, GCF = 4 and LCM = 60. If one number is 20, find the other number.
Solution:
Given: GCF (y, 20) = 4 and LCM (y, 20) = 60
∵ GCF × LCM = 20 × (y)
⇒ y = (GCF × LCM)/20
⇒ y = (4 × 60)/20
⇒ y = 12
Therefore, the other number is 12.Example 2: Find the greatest number that divides 12 and 20 exactly.
Solution:
The greatest number that divides 12 and 20 exactly is their greatest common factor, i.e. GCF of 12 and 20.
⇒ Factors of 12 and 20:- Factors of 12 = 1, 2, 3, 4, 6, 12
- Factors of 20 = 1, 2, 4, 5, 10, 20
Therefore, the GCF of 12 and 20 is 4.
Example 3: The product of two numbers is 240. If their GCF is 4, what is their LCM?
Solution:
Given: GCF = 4 and product of numbers = 240
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 240/4
Therefore, the LCM is 60.
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FAQs on GCF of 12 and 20
What is the GCF of 12 and 20?
The GCF of 12 and 20 is 4. To calculate the GCF (Greatest Common Factor) of 12 and 20, we need to factor each number (factors of 12 = 1, 2, 3, 4, 6, 12; factors of 20 = 1, 2, 4, 5, 10, 20) and choose the greatest factor that exactly divides both 12 and 20, i.e., 4.
What are the Methods to Find GCF of 12 and 20?
There are three commonly used methods to find the GCF of 12 and 20.
- By Prime Factorization
- By Long Division
- By Listing Common Factors
If the GCF of 20 and 12 is 4, Find its LCM.
GCF(20, 12) × LCM(20, 12) = 20 × 12
Since the GCF of 20 and 12 = 4
⇒ 4 × LCM(20, 12) = 240
Therefore, LCM = 60
☛ GCF Calculator
How to Find the GCF of 12 and 20 by Prime Factorization?
To find the GCF of 12 and 20, we will find the prime factorization of the given numbers, i.e. 12 = 2 × 2 × 3; 20 = 2 × 2 × 5.
⇒ Since 2, 2 are common terms in the prime factorization of 12 and 20. Hence, GCF(12, 20) = 2 × 2 = 4
☛ What is a Prime Number?
What is the Relation Between LCM and GCF of 12, 20?
The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 12 and 20, i.e. GCF × LCM = 12 × 20.
How to Find the GCF of 12 and 20 by Long Division Method?
To find the GCF of 12, 20 using long division method, 20 is divided by 12. The corresponding divisor (4) when remainder equals 0 is taken as GCF.
