GCF of 42 and 63
GCF of 42 and 63 is the largest possible number that divides 42 and 63 exactly without any remainder. The factors of 42 and 63 are 1, 2, 3, 6, 7, 14, 21, 42 and 1, 3, 7, 9, 21, 63 respectively. There are 3 commonly used methods to find the GCF of 42 and 63 - Euclidean algorithm, prime factorization, and long division.
| 1. | GCF of 42 and 63 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 42 and 63?
Answer: GCF of 42 and 63 is 21.
Explanation:
The GCF of two non-zero integers, x(42) and y(63), is the greatest positive integer m(21) that divides both x(42) and y(63) without any remainder.
Methods to Find GCF of 42 and 63
The methods to find the GCF of 42 and 63 are explained below.
- Using Euclid's Algorithm
- Listing Common Factors
- Long Division Method
GCF of 42 and 63 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 = 63 and Y = 42
- GCF(63, 42) = GCF(42, 63 mod 42) = GCF(42, 21)
- GCF(42, 21) = GCF(21, 42 mod 21) = GCF(21, 0)
- GCF(21, 0) = 21 (∵ GCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of GCF of 42 and 63 is 21.
GCF of 42 and 63 by Listing Common Factors
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
- Factors of 63: 1, 3, 7, 9, 21, 63
There are 4 common factors of 42 and 63, that are 1, 3, 21, and 7. Therefore, the greatest common factor of 42 and 63 is 21.
GCF of 42 and 63 by Long Division
GCF of 42 and 63 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 63 (larger number) by 42 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (42) by the remainder (21).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (21) is the GCF of 42 and 63.
☛ Also Check:
- GCF of 10 and 30 = 10
- GCF of 56 and 72 = 8
- GCF of 18 and 27 = 9
- GCF of 4 and 9 = 1
- GCF of 54 and 72 = 18
- GCF of 27 and 30 = 3
- GCF of 8 and 14 = 2
FAQs on GCF of 42 and 63
What is the GCF of 42 and 63?
The GCF of 42 and 63 is 21. To calculate the greatest common factor (GCF) of 42 and 63, we need to factor each number (factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42; factors of 63 = 1, 3, 7, 9, 21, 63) and choose the greatest factor that exactly divides both 42 and 63, i.e., 21.
What is the Relation Between LCM and GCF of 42, 63?
The following equation can be used to express the relation between LCM and GCF of 42 and 63, i.e. GCF × LCM = 42 × 63.
How to Find the GCF of 42 and 63 by Prime Factorization?
To find the GCF of 42 and 63, we will find the prime factorization of the given numbers, i.e. 42 = 2 × 3 × 7; 63 = 3 × 3 × 7.
⇒ Since 3, 7 are common terms in the prime factorization of 42 and 63. Hence, GCF(42, 63) = 3 × 7 = 21
☛ Prime Number
What are the Methods to Find GCF of 42 and 63?
There are three commonly used methods to find the GCF of 42 and 63.
- By Listing Common Factors
- By Long Division
- By Prime Factorization
How to Find the GCF of 42 and 63 by Long Division Method?
To find the GCF of 42, 63 using long division method, 63 is divided by 42. The corresponding divisor (21) when remainder equals 0 is taken as GCF.
If the GCF of 63 and 42 is 21, Find its LCM.
GCF(63, 42) × LCM(63, 42) = 63 × 42
Since the GCF of 63 and 42 = 21
⇒ 21 × LCM(63, 42) = 2646
Therefore, LCM = 126
☛ GCF Calculator