GCF of 18 and 42
GCF of 18 and 42 is the largest possible number that divides 18 and 42 exactly without any remainder. The factors of 18 and 42 are 1, 2, 3, 6, 9, 18 and 1, 2, 3, 6, 7, 14, 21, 42 respectively. There are 3 commonly used methods to find the GCF of 18 and 42 - long division, Euclidean algorithm, and prime factorization.
| 1. | GCF of 18 and 42 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 18 and 42?
Answer: GCF of 18 and 42 is 6.
Explanation:
The GCF of two non-zero integers, x(18) and y(42), is the greatest positive integer m(6) that divides both x(18) and y(42) without any remainder.
Methods to Find GCF of 18 and 42
The methods to find the GCF of 18 and 42 are explained below.
- Listing Common Factors
- Prime Factorization Method
- Long Division Method
GCF of 18 and 42 by Listing Common Factors
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
There are 4 common factors of 18 and 42, that are 1, 2, 3, and 6. Therefore, the greatest common factor of 18 and 42 is 6.
GCF of 18 and 42 by Prime Factorization
Prime factorization of 18 and 42 is (2 × 3 × 3) and (2 × 3 × 7) respectively. As visible, 18 and 42 have common prime factors. Hence, the GCF of 18 and 42 is 2 × 3 = 6.
GCF of 18 and 42 by Long Division
GCF of 18 and 42 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 42 (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 42.
☛ Also Check:
- GCF of 28 and 36 = 4
- GCF of 18 and 32 = 2
- GCF of 30 and 36 = 6
- GCF of 13 and 26 = 13
- GCF of 2 and 6 = 2
- GCF of 50 and 72 = 2
- GCF of 12 and 48 = 12
FAQs on GCF of 18 and 42
What is the GCF of 18 and 42?
The GCF of 18 and 42 is 6. To calculate the GCF of 18 and 42, we need to factor each number (factors of 18 = 1, 2, 3, 6, 9, 18; factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42) and choose the greatest factor that exactly divides both 18 and 42, i.e., 6.
How to Find the GCF of 18 and 42 by Prime Factorization?
To find the GCF of 18 and 42, we will find the prime factorization of the given numbers, i.e. 18 = 2 × 3 × 3; 42 = 2 × 3 × 7.
⇒ Since 2, 3 are common terms in the prime factorization of 18 and 42. Hence, GCF(18, 42) = 2 × 3 = 6
☛ Prime Numbers
What is the Relation Between LCM and GCF of 18, 42?
The following equation can be used to express the relation between LCM and GCF of 18 and 42, i.e. GCF × LCM = 18 × 42.
What are the Methods to Find GCF of 18 and 42?
There are three commonly used methods to find the GCF of 18 and 42.
- By Long Division
- By Prime Factorization
- By Listing Common Factors
If the GCF of 42 and 18 is 6, Find its LCM.
GCF(42, 18) × LCM(42, 18) = 42 × 18
Since the GCF of 42 and 18 = 6
⇒ 6 × LCM(42, 18) = 756
Therefore, LCM = 126
☛ GCF Calculator
How to Find the GCF of 18 and 42 by Long Division Method?
To find the GCF of 18, 42 using long division method, 42 is divided by 18. The corresponding divisor (6) when remainder equals 0 is taken as GCF.