GCF of 20 and 42
GCF of 20 and 42 is the largest possible number that divides 20 and 42 exactly without any remainder. The factors of 20 and 42 are 1, 2, 4, 5, 10, 20 and 1, 2, 3, 6, 7, 14, 21, 42 respectively. There are 3 commonly used methods to find the GCF of 20 and 42 - long division, prime factorization, and Euclidean algorithm.
| 1. | GCF of 20 and 42 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 20 and 42?
Answer: GCF of 20 and 42 is 2.
Explanation:
The GCF of two non-zero integers, x(20) and y(42), is the greatest positive integer m(2) that divides both x(20) and y(42) without any remainder.
Methods to Find GCF of 20 and 42
The methods to find the GCF of 20 and 42 are explained below.
- Listing Common Factors
- Long Division Method
- Prime Factorization Method
GCF of 20 and 42 by Listing Common Factors
- Factors of 20: 1, 2, 4, 5, 10, 20
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
There are 2 common factors of 20 and 42, that are 1 and 2. Therefore, the greatest common factor of 20 and 42 is 2.
GCF of 20 and 42 by Long Division
GCF of 20 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 20 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (20) by the remainder (2).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (2) is the GCF of 20 and 42.
GCF of 20 and 42 by Prime Factorization
Prime factorization of 20 and 42 is (2 × 2 × 5) and (2 × 3 × 7) respectively. As visible, 20 and 42 have only one common prime factor i.e. 2. Hence, the GCF of 20 and 42 is 2.
☛ Also Check:
- GCF of 20 and 32 = 4
- GCF of 49 and 98 = 49
- GCF of 24 and 28 = 4
- GCF of 15 and 18 = 3
- GCF of 40 and 56 = 8
- GCF of 48 and 84 = 12
- GCF of 26 and 91 = 13
FAQs on GCF of 20 and 42
What is the GCF of 20 and 42?
The GCF of 20 and 42 is 2. To calculate the greatest common factor (GCF) of 20 and 42, we need to factor each number (factors of 20 = 1, 2, 4, 5, 10, 20; factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42) and choose the greatest factor that exactly divides both 20 and 42, i.e., 2.
What are the Methods to Find GCF of 20 and 42?
There are three commonly used methods to find the GCF of 20 and 42.
- By Prime Factorization
- By Long Division
- By Euclidean Algorithm
If the GCF of 42 and 20 is 2, Find its LCM.
GCF(42, 20) × LCM(42, 20) = 42 × 20
Since the GCF of 42 and 20 = 2
⇒ 2 × LCM(42, 20) = 840
Therefore, LCM = 420
☛ Greatest Common Factor Calculator
How to Find the GCF of 20 and 42 by Long Division Method?
To find the GCF of 20, 42 using long division method, 42 is divided by 20. The corresponding divisor (2) when remainder equals 0 is taken as GCF.
How to Find the GCF of 20 and 42 by Prime Factorization?
To find the GCF of 20 and 42, we will find the prime factorization of the given numbers, i.e. 20 = 2 × 2 × 5; 42 = 2 × 3 × 7.
⇒ Since 2 is the only common prime factor of 20 and 42. Hence, GCF (20, 42) = 2.
☛ Prime Numbers
What is the Relation Between LCM and GCF of 20, 42?
The following equation can be used to express the relation between LCM and GCF of 20 and 42, i.e. GCF × LCM = 20 × 42.