GCF of 18 and 24 is the largest possible number that divides 18 and 24 exactly without any remainder. The factors of 18 and 24 are 1, 2, 3, 6, 9, 18 and 1, 2, 3, 4, 6, 8, 12, 24 respectively. There are 3 commonly used methods to find the GCF of 18 and 24 - Euclidean algorithm, prime factorization, and long division.
| 1. | GCF of 18 and 24 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 18 and 24?
Answer: GCF of 18 and 24 is 6.
Explanation:
The GCF of two non-zero integers, x(18) and y(24), is the greatest positive integer m(6) that divides both x(18) and y(24) without any remainder.
Methods to Find GCF of 18 and 24
Let's look at the different methods for finding the GCF of 18 and 24.
- Prime Factorization Method
- Long Division Method
- Listing Common Factors
GCF of 18 and 24 by Prime Factorization
Prime factorization of 18 and 24 is (2 × 3 × 3) and (2 × 2 × 2 × 3) respectively. As visible, 18 and 24 have common prime factors. Hence, the GCF of 18 and 24 is 2 × 3 = 6.
GCF of 18 and 24 by Long Division
GCF of 18 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 18 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (18) by the remainder (6).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (6) is the GCF of 18 and 24.
GCF of 18 and 24 by Listing Common Factors
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
There are 4 common factors of 18 and 24, that are 1, 2, 3, and 6. Therefore, the greatest common factor of 18 and 24 is 6.
☛ Also Check:
- GCF of 10 and 15 = 5
- GCF of 30 and 70 = 10
- GCF of 20 and 32 = 4
- GCF of 2 and 7 = 1
- GCF of 36 and 45 = 9
- GCF of 18 and 27 = 9
- GCF of 3 and 7 = 1
GCF of 18 and 24 Examples
Example 1: Find the greatest number that divides 18 and 24 exactly.
Solution:
The greatest number that divides 18 and 24 exactly is their greatest common factor, i.e. GCF of 18 and 24.
⇒ Factors of 18 and 24:- Factors of 18 = 1, 2, 3, 6, 9, 18
- Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
Therefore, the GCF of 18 and 24 is 6.
Example 2: The product of two numbers is 432. If their GCF is 6, what is their LCM?
Solution:
Given: GCF = 6 and product of numbers = 432
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 432/6
Therefore, the LCM is 72.Example 3: Find the GCF of 18 and 24, if their LCM is 72.
Solution:
∵ LCM × GCF = 18 × 24
⇒ GCF(18, 24) = (18 × 24)/72 = 6
Therefore, the greatest common factor of 18 and 24 is 6.
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FAQs on GCF of 18 and 24
What is the GCF of 18 and 24?
The GCF of 18 and 24 is 6. To calculate the greatest common factor of 18 and 24, we need to factor each number (factors of 18 = 1, 2, 3, 6, 9, 18; factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24) and choose the greatest factor that exactly divides both 18 and 24, i.e., 6.
What are the Methods to Find GCF of 18 and 24?
There are three commonly used methods to find the GCF of 18 and 24.
- By Prime Factorization
- By Euclidean Algorithm
- By Long Division
What is the Relation Between LCM and GCF of 18, 24?
The following equation can be used to express the relation between LCM and GCF of 18 and 24, i.e. GCF × LCM = 18 × 24.
How to Find the GCF of 18 and 24 by Long Division Method?
To find the GCF of 18, 24 using long division method, 24 is divided by 18. The corresponding divisor (6) when remainder equals 0 is taken as GCF.
How to Find the GCF of 18 and 24 by Prime Factorization?
To find the GCF of 18 and 24, we will find the prime factorization of the given numbers, i.e. 18 = 2 × 3 × 3; 24 = 2 × 2 × 2 × 3.
⇒ Since 2, 3 are common terms in the prime factorization of 18 and 24. Hence, GCF(18, 24) = 2 × 3 = 6
☛ Prime Number
If the GCF of 24 and 18 is 6, Find its LCM.
GCF(24, 18) × LCM(24, 18) = 24 × 18
Since the GCF of 24 and 18 = 6
⇒ 6 × LCM(24, 18) = 432
Therefore, LCM = 72
☛ Greatest Common Factor Calculator
