GCF of 18 and 27
GCF of 18 and 27 is the largest possible number that divides 18 and 27 exactly without any remainder. The factors of 18 and 27 are 1, 2, 3, 6, 9, 18 and 1, 3, 9, 27 respectively. There are 3 commonly used methods to find the GCF of 18 and 27 - long division, Euclidean algorithm, and prime factorization.
| 1. | GCF of 18 and 27 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 18 and 27?
Answer: GCF of 18 and 27 is 9.
Explanation:
The GCF of two non-zero integers, x(18) and y(27), is the greatest positive integer m(9) that divides both x(18) and y(27) without any remainder.
Methods to Find GCF of 18 and 27
Let's look at the different methods for finding the GCF of 18 and 27.
- Listing Common Factors
- Long Division Method
- Prime Factorization Method
GCF of 18 and 27 by Listing Common Factors
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 27: 1, 3, 9, 27
There are 3 common factors of 18 and 27, that are 1, 3, and 9. Therefore, the greatest common factor of 18 and 27 is 9.
GCF of 18 and 27 by Long Division
GCF of 18 and 27 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 27 (larger number) by 18 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (18) by the remainder (9).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (9) is the GCF of 18 and 27.
GCF of 18 and 27 by Prime Factorization
Prime factorization of 18 and 27 is (2 × 3 × 3) and (3 × 3 × 3) respectively. As visible, 18 and 27 have common prime factors. Hence, the GCF of 18 and 27 is 3 × 3 = 9.
☛ Also Check:
- GCF of 30 and 105 = 15
- GCF of 28 and 49 = 7
- GCF of 30 and 48 = 6
- GCF of 10 and 14 = 2
- GCF of 35 and 45 = 5
- GCF of 175 and 25 = 25
- GCF of 4 and 12 = 4
FAQs on GCF of 18 and 27
What is the GCF of 18 and 27?
The GCF of 18 and 27 is 9. To calculate the greatest common factor (GCF) of 18 and 27, we need to factor each number (factors of 18 = 1, 2, 3, 6, 9, 18; factors of 27 = 1, 3, 9, 27) and choose the greatest factor that exactly divides both 18 and 27, i.e., 9.
How to Find the GCF of 18 and 27 by Long Division Method?
To find the GCF of 18, 27 using long division method, 27 is divided by 18. The corresponding divisor (9) when remainder equals 0 is taken as GCF.
What is the Relation Between LCM and GCF of 18, 27?
The following equation can be used to express the relation between Least Common Multiple and GCF of 18 and 27, i.e. GCF × LCM = 18 × 27.
If the GCF of 27 and 18 is 9, Find its LCM.
GCF(27, 18) × LCM(27, 18) = 27 × 18
Since the GCF of 27 and 18 = 9
⇒ 9 × LCM(27, 18) = 486
Therefore, LCM = 54
☛ Greatest Common Factor Calculator
How to Find the GCF of 18 and 27 by Prime Factorization?
To find the GCF of 18 and 27, we will find the prime factorization of the given numbers, i.e. 18 = 2 × 3 × 3; 27 = 3 × 3 × 3.
⇒ Since 3, 3 are common terms in the prime factorization of 18 and 27. Hence, GCF(18, 27) = 3 × 3 = 9
☛ Prime Numbers
What are the Methods to Find GCF of 18 and 27?
There are three commonly used methods to find the GCF of 18 and 27.
- By Long Division
- By Prime Factorization
- By Listing Common Factors