GCF of 20 and 24 is the largest possible number that divides 20 and 24 exactly without any remainder. The factors of 20 and 24 are 1, 2, 4, 5, 10, 20 and 1, 2, 3, 4, 6, 8, 12, 24 respectively. There are 3 commonly used methods to find the GCF of 20 and 24 - prime factorization, Euclidean algorithm, and long division.
| 1. | GCF of 20 and 24 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 20 and 24?
Answer: GCF of 20 and 24 is 4.
Explanation:
The GCF of two non-zero integers, x(20) and y(24), is the greatest positive integer m(4) that divides both x(20) and y(24) without any remainder.
Methods to Find GCF of 20 and 24
Let's look at the different methods for finding the GCF of 20 and 24.
- Long Division Method
- Using Euclid's Algorithm
- Prime Factorization Method
GCF of 20 and 24 by Long Division
GCF of 20 and 24 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 24 (larger number) by 20 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (20) by the remainder (4).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (4) is the GCF of 20 and 24.
GCF of 20 and 24 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 = 24 and Y = 20
- GCF(24, 20) = GCF(20, 24 mod 20) = GCF(20, 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 20 and 24 is 4.
GCF of 20 and 24 by Prime Factorization
Prime factorization of 20 and 24 is (2 × 2 × 5) and (2 × 2 × 2 × 3) respectively. As visible, 20 and 24 have common prime factors. Hence, the GCF of 20 and 24 is 2 × 2 = 4.
☛ Also Check:
- GCF of 15 and 24 = 3
- GCF of 84 and 90 = 6
- GCF of 18 and 30 = 6
- GCF of 27 and 64 = 1
- GCF of 108 and 24 = 12
- GCF of 9 and 15 = 3
- GCF of 12 and 16 = 4
GCF of 20 and 24 Examples
Example 1: For two numbers, GCF = 4 and LCM = 120. If one number is 24, find the other number.
Solution:
Given: GCF (z, 24) = 4 and LCM (z, 24) = 120
∵ GCF × LCM = 24 × (z)
⇒ z = (GCF × LCM)/24
⇒ z = (4 × 120)/24
⇒ z = 20
Therefore, the other number is 20.Example 2: The product of two numbers is 480. If their GCF is 4, what is their LCM?
Solution:
Given: GCF = 4 and product of numbers = 480
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 480/4
Therefore, the LCM is 120.Example 3: Find the greatest number that divides 20 and 24 exactly.
Solution:
The greatest number that divides 20 and 24 exactly is their greatest common factor, i.e. GCF of 20 and 24.
⇒ Factors of 20 and 24:- Factors of 20 = 1, 2, 4, 5, 10, 20
- Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
Therefore, the GCF of 20 and 24 is 4.
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FAQs on GCF of 20 and 24
What is the GCF of 20 and 24?
The GCF of 20 and 24 is 4. To calculate the GCF (Greatest Common Factor) of 20 and 24, we need to factor each number (factors of 20 = 1, 2, 4, 5, 10, 20; factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24) and choose the greatest factor that exactly divides both 20 and 24, i.e., 4.
How to Find the GCF of 20 and 24 by Long Division Method?
To find the GCF of 20, 24 using long division method, 24 is divided by 20. The corresponding divisor (4) when remainder equals 0 is taken as GCF.
What are the Methods to Find GCF of 20 and 24?
There are three commonly used methods to find the GCF of 20 and 24.
- By Listing Common Factors
- By Long Division
- By Prime Factorization
How to Find the GCF of 20 and 24 by Prime Factorization?
To find the GCF of 20 and 24, we will find the prime factorization of the given numbers, i.e. 20 = 2 × 2 × 5; 24 = 2 × 2 × 2 × 3.
⇒ Since 2, 2 are common terms in the prime factorization of 20 and 24. Hence, GCF(20, 24) = 2 × 2 = 4
☛ What are Prime Numbers?
If the GCF of 24 and 20 is 4, Find its LCM.
GCF(24, 20) × LCM(24, 20) = 24 × 20
Since the GCF of 24 and 20 = 4
⇒ 4 × LCM(24, 20) = 480
Therefore, LCM = 120
☛ Greatest Common Factor Calculator
What is the Relation Between LCM and GCF of 20, 24?
The following equation can be used to express the relation between Least Common Multiple and GCF of 20 and 24, i.e. GCF × LCM = 20 × 24.
