GCF of 18 and 14
GCF of 18 and 14 is the largest possible number that divides 18 and 14 exactly without any remainder. The factors of 18 and 14 are 1, 2, 3, 6, 9, 18 and 1, 2, 7, 14 respectively. There are 3 commonly used methods to find the GCF of 18 and 14 - prime factorization, long division, and Euclidean algorithm.
| 1. | GCF of 18 and 14 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 18 and 14?
Answer: GCF of 18 and 14 is 2.
Explanation:
The GCF of two non-zero integers, x(18) and y(14), is the greatest positive integer m(2) that divides both x(18) and y(14) without any remainder.
Methods to Find GCF of 18 and 14
The methods to find the GCF of 18 and 14 are explained below.
- Long Division Method
- Prime Factorization Method
- Listing Common Factors
GCF of 18 and 14 by Long Division
GCF of 18 and 14 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 18 (larger number) by 14 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (14) by the remainder (4).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (2) is the GCF of 18 and 14.
GCF of 18 and 14 by Prime Factorization
Prime factorization of 18 and 14 is (2 × 3 × 3) and (2 × 7) respectively. As visible, 18 and 14 have only one common prime factor i.e. 2. Hence, the GCF of 18 and 14 is 2.
GCF of 18 and 14 by Listing Common Factors
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 14: 1, 2, 7, 14
There are 2 common factors of 18 and 14, that are 1 and 2. Therefore, the greatest common factor of 18 and 14 is 2.
☛ Also Check:
- GCF of 48 and 64 = 16
- GCF of 48 and 72 = 24
- GCF of 15 and 75 = 15
- GCF of 84 and 105 = 21
- GCF of 72 and 36 = 36
- GCF of 6 and 24 = 6
- GCF of 15 and 50 = 5
FAQs on GCF of 18 and 14
What is the GCF of 18 and 14?
The GCF of 18 and 14 is 2. To calculate the greatest common factor of 18 and 14, we need to factor each number (factors of 18 = 1, 2, 3, 6, 9, 18; factors of 14 = 1, 2, 7, 14) and choose the greatest factor that exactly divides both 18 and 14, i.e., 2.
How to Find the GCF of 18 and 14 by Prime Factorization?
To find the GCF of 18 and 14, we will find the prime factorization of the given numbers, i.e. 18 = 2 × 3 × 3; 14 = 2 × 7.
⇒ Since 2 is the only common prime factor of 18 and 14. Hence, GCF (18, 14) = 2.
☛ What is a Prime Number?
What are the Methods to Find GCF of 18 and 14?
There are three commonly used methods to find the GCF of 18 and 14.
- By Euclidean Algorithm
- By Prime Factorization
- By Long Division
What is the Relation Between LCM and GCF of 18, 14?
The following equation can be used to express the relation between LCM and GCF of 18 and 14, i.e. GCF × LCM = 18 × 14.
If the GCF of 14 and 18 is 2, Find its LCM.
GCF(14, 18) × LCM(14, 18) = 14 × 18
Since the GCF of 14 and 18 = 2
⇒ 2 × LCM(14, 18) = 252
Therefore, LCM = 126
☛ GCF Calculator
How to Find the GCF of 18 and 14 by Long Division Method?
To find the GCF of 18, 14 using long division method, 18 is divided by 14. The corresponding divisor (2) when remainder equals 0 is taken as GCF.