GCF of 21 and 42
GCF of 21 and 42 is the largest possible number that divides 21 and 42 exactly without any remainder. The factors of 21 and 42 are 1, 3, 7, 21 and 1, 2, 3, 6, 7, 14, 21, 42 respectively. There are 3 commonly used methods to find the GCF of 21 and 42 - Euclidean algorithm, prime factorization, and long division.
| 1. | GCF of 21 and 42 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 21 and 42?
Answer: GCF of 21 and 42 is 21.
Explanation:
The GCF of two non-zero integers, x(21) and y(42), is the greatest positive integer m(21) that divides both x(21) and y(42) without any remainder.
Methods to Find GCF of 21 and 42
Let's look at the different methods for finding the GCF of 21 and 42.
- Listing Common Factors
- Long Division Method
- Prime Factorization Method
GCF of 21 and 42 by Listing Common Factors
- Factors of 21: 1, 3, 7, 21
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
There are 4 common factors of 21 and 42, that are 1, 3, 21, and 7. Therefore, the greatest common factor of 21 and 42 is 21.
GCF of 21 and 42 by Long Division
GCF of 21 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 21 (smaller number).
- Step 2: Since the remainder = 0, the divisor (21) is the GCF of 21 and 42.
The corresponding divisor (21) is the GCF of 21 and 42.
GCF of 21 and 42 by Prime Factorization
Prime factorization of 21 and 42 is (3 × 7) and (2 × 3 × 7) respectively. As visible, 21 and 42 have common prime factors. Hence, the GCF of 21 and 42 is 3 × 7 = 21.
☛ Also Check:
- GCF of 24 and 60 = 12
- GCF of 15 and 35 = 5
- GCF of 24 and 48 = 24
- GCF of 7 and 56 = 7
- GCF of 64 and 32 = 32
- GCF of 8 and 10 = 2
- GCF of 9 and 16 = 1
FAQs on GCF of 21 and 42
What is the GCF of 21 and 42?
The GCF of 21 and 42 is 21. To calculate the greatest common factor of 21 and 42, we need to factor each number (factors of 21 = 1, 3, 7, 21; factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42) and choose the greatest factor that exactly divides both 21 and 42, i.e., 21.
How to Find the GCF of 21 and 42 by Prime Factorization?
To find the GCF of 21 and 42, we will find the prime factorization of the given numbers, i.e. 21 = 3 × 7; 42 = 2 × 3 × 7.
⇒ Since 3, 7 are common terms in the prime factorization of 21 and 42. Hence, GCF(21, 42) = 3 × 7 = 21
☛ What are Prime Numbers?
What is the Relation Between LCM and GCF of 21, 42?
The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 21 and 42, i.e. GCF × LCM = 21 × 42.
How to Find the GCF of 21 and 42 by Long Division Method?
To find the GCF of 21, 42 using long division method, 42 is divided by 21. The corresponding divisor (21) when remainder equals 0 is taken as GCF.
What are the Methods to Find GCF of 21 and 42?
There are three commonly used methods to find the GCF of 21 and 42.
- By Long Division
- By Euclidean Algorithm
- By Prime Factorization
If the GCF of 42 and 21 is 21, Find its LCM.
GCF(42, 21) × LCM(42, 21) = 42 × 21
Since the GCF of 42 and 21 = 21
⇒ 21 × LCM(42, 21) = 882
Therefore, LCM = 42
☛ Greatest Common Factor Calculator