GCF of 12 and 42
GCF of 12 and 42 is the largest possible number that divides 12 and 42 exactly without any remainder. The factors of 12 and 42 are 1, 2, 3, 4, 6, 12 and 1, 2, 3, 6, 7, 14, 21, 42 respectively. There are 3 commonly used methods to find the GCF of 12 and 42 - prime factorization, Euclidean algorithm, and long division.
| 1. | GCF of 12 and 42 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 12 and 42?
Answer: GCF of 12 and 42 is 6.
Explanation:
The GCF of two non-zero integers, x(12) and y(42), is the greatest positive integer m(6) that divides both x(12) and y(42) without any remainder.
Methods to Find GCF of 12 and 42
Let's look at the different methods for finding the GCF of 12 and 42.
- Listing Common Factors
- Prime Factorization Method
- Using Euclid's Algorithm
GCF of 12 and 42 by Listing Common Factors
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
There are 4 common factors of 12 and 42, that are 1, 2, 3, and 6. Therefore, the greatest common factor of 12 and 42 is 6.
GCF of 12 and 42 by Prime Factorization
Prime factorization of 12 and 42 is (2 × 2 × 3) and (2 × 3 × 7) respectively. As visible, 12 and 42 have common prime factors. Hence, the GCF of 12 and 42 is 2 × 3 = 6.
GCF of 12 and 42 by Euclidean Algorithm
As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.
Here X = 42 and Y = 12
- GCF(42, 12) = GCF(12, 42 mod 12) = GCF(12, 6)
- GCF(12, 6) = GCF(6, 12 mod 6) = GCF(6, 0)
- GCF(6, 0) = 6 (∵ GCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of GCF of 12 and 42 is 6.
☛ Also Check:
- GCF of 72 and 80 = 8
- GCF of 63 and 54 = 9
- GCF of 20 and 32 = 4
- GCF of 6 and 21 = 3
- GCF of 7 and 8 = 1
- GCF of 9 and 30 = 3
- GCF of 12 and 13 = 1
FAQs on GCF of 12 and 42
What is the GCF of 12 and 42?
The GCF of 12 and 42 is 6. To calculate the greatest common factor (GCF) of 12 and 42, we need to factor each number (factors of 12 = 1, 2, 3, 4, 6, 12; factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42) and choose the greatest factor that exactly divides both 12 and 42, i.e., 6.
If the GCF of 42 and 12 is 6, Find its LCM.
GCF(42, 12) × LCM(42, 12) = 42 × 12
Since the GCF of 42 and 12 = 6
⇒ 6 × LCM(42, 12) = 504
Therefore, LCM = 84
☛ Greatest Common Factor Calculator
How to Find the GCF of 12 and 42 by Long Division Method?
To find the GCF of 12, 42 using long division method, 42 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 42?
There are three commonly used methods to find the GCF of 12 and 42.
- By Long Division
- By Prime Factorization
- By Listing Common Factors
How to Find the GCF of 12 and 42 by Prime Factorization?
To find the GCF of 12 and 42, we will find the prime factorization of the given numbers, i.e. 12 = 2 × 2 × 3; 42 = 2 × 3 × 7.
⇒ Since 2, 3 are common terms in the prime factorization of 12 and 42. Hence, GCF(12, 42) = 2 × 3 = 6
☛ Prime Number
What is the Relation Between LCM and GCF of 12, 42?
The following equation can be used to express the relation between LCM and GCF of 12 and 42, i.e. GCF × LCM = 12 × 42.