GCF of 12 and 18
GCF of 12 and 18 is the largest possible number that divides 12 and 18 exactly without any remainder. The factors of 12 and 18 are 1, 2, 3, 4, 6, 12 and 1, 2, 3, 6, 9, 18 respectively. There are 3 commonly used methods to find the GCF of 12 and 18 - prime factorization, long division, and Euclidean algorithm.
| 1. | GCF of 12 and 18 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 12 and 18?
Answer: GCF of 12 and 18 is 6.
Explanation:
The GCF of two non-zero integers, x(12) and y(18), is the greatest positive integer m(6) that divides both x(12) and y(18) without any remainder.
Methods to Find GCF of 12 and 18
Let's look at the different methods for finding the GCF of 12 and 18.
- Long Division Method
- Prime Factorization Method
- Listing Common Factors
GCF of 12 and 18 by Long Division
GCF of 12 and 18 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 18 (larger number) by 12 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (12) by the remainder (6).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (6) is the GCF of 12 and 18.
GCF of 12 and 18 by Prime Factorization
Prime factorization of 12 and 18 is (2 × 2 × 3) and (2 × 3 × 3) respectively. As visible, 12 and 18 have common prime factors. Hence, the GCF of 12 and 18 is 2 × 3 = 6.
GCF of 12 and 18 by Listing Common Factors
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 18: 1, 2, 3, 6, 9, 18
There are 4 common factors of 12 and 18, that are 1, 2, 3, and 6. Therefore, the greatest common factor of 12 and 18 is 6.
☛ Also Check:
- GCF of 18 and 32 = 2
- GCF of 21 and 84 = 21
- GCF of 36 and 100 = 4
- GCF of 12 and 48 = 12
- GCF of 18 and 35 = 1
- GCF of 18 and 63 = 9
- GCF of 48 and 56 = 8
FAQs on GCF of 12 and 18
What is the GCF of 12 and 18?
The GCF of 12 and 18 is 6. To calculate the GCF (Greatest Common Factor) of 12 and 18, we need to factor each number (factors of 12 = 1, 2, 3, 4, 6, 12; factors of 18 = 1, 2, 3, 6, 9, 18) and choose the greatest factor that exactly divides both 12 and 18, i.e., 6.
What is the Relation Between LCM and GCF of 12, 18?
The following equation can be used to express the relation between LCM and GCF of 12 and 18, i.e. GCF × LCM = 12 × 18.
How to Find the GCF of 12 and 18 by Long Division Method?
To find the GCF of 12, 18 using long division method, 18 is divided by 12. The corresponding divisor (6) when remainder equals 0 is taken as GCF.
What are the Methods to Find GCF of 12 and 18?
There are three commonly used methods to find the GCF of 12 and 18.
- By Prime Factorization
- By Euclidean Algorithm
- By Long Division
How to Find the GCF of 12 and 18 by Prime Factorization?
To find the GCF of 12 and 18, we will find the prime factorization of the given numbers, i.e. 12 = 2 × 2 × 3; 18 = 2 × 3 × 3.
⇒ Since 2, 3 are common terms in the prime factorization of 12 and 18. Hence, GCF(12, 18) = 2 × 3 = 6
☛ What are Prime Numbers?
If the GCF of 18 and 12 is 6, Find its LCM.
GCF(18, 12) × LCM(18, 12) = 18 × 12
Since the GCF of 18 and 12 = 6
⇒ 6 × LCM(18, 12) = 216
Therefore, LCM = 36
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