GCF of 18 and 54
GCF of 18 and 54 is the largest possible number that divides 18 and 54 exactly without any remainder. The factors of 18 and 54 are 1, 2, 3, 6, 9, 18 and 1, 2, 3, 6, 9, 18, 27, 54 respectively. There are 3 commonly used methods to find the GCF of 18 and 54 - long division, prime factorization, and Euclidean algorithm.
| 1. | GCF of 18 and 54 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 18 and 54?
Answer: GCF of 18 and 54 is 18.
Explanation:
The GCF of two non-zero integers, x(18) and y(54), is the greatest positive integer m(18) that divides both x(18) and y(54) without any remainder.
Methods to Find GCF of 18 and 54
Let's look at the different methods for finding the GCF of 18 and 54.
- Prime Factorization Method
- Listing Common Factors
- Long Division Method
GCF of 18 and 54 by Prime Factorization
Prime factorization of 18 and 54 is (2 × 3 × 3) and (2 × 3 × 3 × 3) respectively. As visible, 18 and 54 have common prime factors. Hence, the GCF of 18 and 54 is 2 × 3 × 3 = 18.
GCF of 18 and 54 by Listing Common Factors
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
There are 6 common factors of 18 and 54, that are 1, 2, 3, 6, 9, and 18. Therefore, the greatest common factor of 18 and 54 is 18.
GCF of 18 and 54 by Long Division
GCF of 18 and 54 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 54 (larger number) by 18 (smaller number).
- Step 2: Since the remainder = 0, the divisor (18) is the GCF of 18 and 54.
The corresponding divisor (18) is the GCF of 18 and 54.
☛ Also Check:
- GCF of 77 and 56 = 7
- GCF of 12 and 32 = 4
- GCF of 21 and 30 = 3
- GCF of 15 and 18 = 3
- GCF of 15 and 35 = 5
- GCF of 24 and 64 = 8
- GCF of 60 and 60 = 60
FAQs on GCF of 18 and 54
What is the GCF of 18 and 54?
The GCF of 18 and 54 is 18. To calculate the GCF of 18 and 54, we need to factor each number (factors of 18 = 1, 2, 3, 6, 9, 18; factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54) and choose the greatest factor that exactly divides both 18 and 54, i.e., 18.
How to Find the GCF of 18 and 54 by Prime Factorization?
To find the GCF of 18 and 54, we will find the prime factorization of the given numbers, i.e. 18 = 2 × 3 × 3; 54 = 2 × 3 × 3 × 3.
⇒ Since 2, 3, 3 are common terms in the prime factorization of 18 and 54. Hence, GCF(18, 54) = 2 × 3 × 3 = 18
☛ Prime Number
How to Find the GCF of 18 and 54 by Long Division Method?
To find the GCF of 18, 54 using long division method, 54 is divided by 18. The corresponding divisor (18) when remainder equals 0 is taken as GCF.
If the GCF of 54 and 18 is 18, Find its LCM.
GCF(54, 18) × LCM(54, 18) = 54 × 18
Since the GCF of 54 and 18 = 18
⇒ 18 × LCM(54, 18) = 972
Therefore, LCM = 54
☛ Greatest Common Factor Calculator
What are the Methods to Find GCF of 18 and 54?
There are three commonly used methods to find the GCF of 18 and 54.
- By Long Division
- By Listing Common Factors
- By Prime Factorization
What is the Relation Between LCM and GCF of 18, 54?
The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 18 and 54, i.e. GCF × LCM = 18 × 54.