GCF of 14 and 42
GCF of 14 and 42 is the largest possible number that divides 14 and 42 exactly without any remainder. The factors of 14 and 42 are 1, 2, 7, 14 and 1, 2, 3, 6, 7, 14, 21, 42 respectively. There are 3 commonly used methods to find the GCF of 14 and 42 - Euclidean algorithm, prime factorization, and long division.
| 1. | GCF of 14 and 42 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 14 and 42?
Answer: GCF of 14 and 42 is 14.
Explanation:
The GCF of two non-zero integers, x(14) and y(42), is the greatest positive integer m(14) that divides both x(14) and y(42) without any remainder.
Methods to Find GCF of 14 and 42
The methods to find the GCF of 14 and 42 are explained below.
- Prime Factorization Method
- Long Division Method
- Listing Common Factors
GCF of 14 and 42 by Prime Factorization
Prime factorization of 14 and 42 is (2 × 7) and (2 × 3 × 7) respectively. As visible, 14 and 42 have common prime factors. Hence, the GCF of 14 and 42 is 2 × 7 = 14.
GCF of 14 and 42 by Long Division
GCF of 14 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 14 (smaller number).
- Step 2: Since the remainder = 0, the divisor (14) is the GCF of 14 and 42.
The corresponding divisor (14) is the GCF of 14 and 42.
GCF of 14 and 42 by Listing Common Factors
- Factors of 14: 1, 2, 7, 14
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
There are 4 common factors of 14 and 42, that are 1, 2, 14, and 7. Therefore, the greatest common factor of 14 and 42 is 14.
☛ Also Check:
- GCF of 25 and 75 = 25
- GCF of 15 and 40 = 5
- GCF of 42 and 60 = 6
- GCF of 10 and 20 = 10
- GCF of 75 and 125 = 25
- GCF of 10 and 35 = 5
- GCF of 8 and 20 = 4
FAQs on GCF of 14 and 42
What is the GCF of 14 and 42?
The GCF of 14 and 42 is 14. To calculate the GCF of 14 and 42, we need to factor each number (factors of 14 = 1, 2, 7, 14; factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42) and choose the greatest factor that exactly divides both 14 and 42, i.e., 14.
How to Find the GCF of 14 and 42 by Prime Factorization?
To find the GCF of 14 and 42, we will find the prime factorization of the given numbers, i.e. 14 = 2 × 7; 42 = 2 × 3 × 7.
⇒ Since 2, 7 are common terms in the prime factorization of 14 and 42. Hence, GCF(14, 42) = 2 × 7 = 14
☛ What are Prime Numbers?
What is the Relation Between LCM and GCF of 14, 42?
The following equation can be used to express the relation between LCM and GCF of 14 and 42, i.e. GCF × LCM = 14 × 42.
What are the Methods to Find GCF of 14 and 42?
There are three commonly used methods to find the GCF of 14 and 42.
- By Listing Common Factors
- By Long Division
- By Prime Factorization
How to Find the GCF of 14 and 42 by Long Division Method?
To find the GCF of 14, 42 using long division method, 42 is divided by 14. The corresponding divisor (14) when remainder equals 0 is taken as GCF.
If the GCF of 42 and 14 is 14, Find its LCM.
GCF(42, 14) × LCM(42, 14) = 42 × 14
Since the GCF of 42 and 14 = 14
⇒ 14 × LCM(42, 14) = 588
Therefore, LCM = 42
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