GCF of 6 and 42
GCF of 6 and 42 is the largest possible number that divides 6 and 42 exactly without any remainder. The factors of 6 and 42 are 1, 2, 3, 6 and 1, 2, 3, 6, 7, 14, 21, 42 respectively. There are 3 commonly used methods to find the GCF of 6 and 42 - Euclidean algorithm, long division, and prime factorization.
| 1. | GCF of 6 and 42 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 6 and 42?
Answer: GCF of 6 and 42 is 6.
Explanation:
The GCF of two non-zero integers, x(6) and y(42), is the greatest positive integer m(6) that divides both x(6) and y(42) without any remainder.
Methods to Find GCF of 6 and 42
The methods to find the GCF of 6 and 42 are explained below.
- Listing Common Factors
- Long Division Method
- Using Euclid's Algorithm
GCF of 6 and 42 by Listing Common Factors
- Factors of 6: 1, 2, 3, 6
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
There are 4 common factors of 6 and 42, that are 1, 2, 3, and 6. Therefore, the greatest common factor of 6 and 42 is 6.
GCF of 6 and 42 by Long Division
GCF of 6 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 6 (smaller number).
- Step 2: Since the remainder = 0, the divisor (6) is the GCF of 6 and 42.
The corresponding divisor (6) is the GCF of 6 and 42.
GCF of 6 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 = 6
- GCF(42, 6) = GCF(6, 42 mod 6) = GCF(6, 0)
- GCF(6, 0) = 6 (∵ GCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of GCF of 6 and 42 is 6.
☛ Also Check:
- GCF of 21 and 63 = 21
- GCF of 42 and 63 = 21
- GCF of 40 and 56 = 8
- GCF of 18 and 27 = 9
- GCF of 50 and 75 = 25
- GCF of 30 and 50 = 10
- GCF of 8 and 12 = 4
FAQs on GCF of 6 and 42
What is the GCF of 6 and 42?
The GCF of 6 and 42 is 6. To calculate the greatest common factor of 6 and 42, we need to factor each number (factors of 6 = 1, 2, 3, 6; factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42) and choose the greatest factor that exactly divides both 6 and 42, i.e., 6.
What are the Methods to Find GCF of 6 and 42?
There are three commonly used methods to find the GCF of 6 and 42.
- By Prime Factorization
- By Long Division
- By Listing Common Factors
How to Find the GCF of 6 and 42 by Long Division Method?
To find the GCF of 6, 42 using long division method, 42 is divided by 6. The corresponding divisor (6) when remainder equals 0 is taken as GCF.
If the GCF of 42 and 6 is 6, Find its LCM.
GCF(42, 6) × LCM(42, 6) = 42 × 6
Since the GCF of 42 and 6 = 6
⇒ 6 × LCM(42, 6) = 252
Therefore, LCM = 42
☛ Greatest Common Factor Calculator
How to Find the GCF of 6 and 42 by Prime Factorization?
To find the GCF of 6 and 42, we will find the prime factorization of the given numbers, i.e. 6 = 2 × 3; 42 = 2 × 3 × 7.
⇒ Since 2, 3 are common terms in the prime factorization of 6 and 42. Hence, GCF(6, 42) = 2 × 3 = 6
☛ Prime Numbers
What is the Relation Between LCM and GCF of 6, 42?
The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 6 and 42, i.e. GCF × LCM = 6 × 42.