GCF of 7 and 63
GCF of 7 and 63 is the largest possible number that divides 7 and 63 exactly without any remainder. The factors of 7 and 63 are 1, 7 and 1, 3, 7, 9, 21, 63 respectively. There are 3 commonly used methods to find the GCF of 7 and 63 - prime factorization, Euclidean algorithm, and long division.
| 1. | GCF of 7 and 63 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 7 and 63?
Answer: GCF of 7 and 63 is 7.
Explanation:
The GCF of two non-zero integers, x(7) and y(63), is the greatest positive integer m(7) that divides both x(7) and y(63) without any remainder.
Methods to Find GCF of 7 and 63
The methods to find the GCF of 7 and 63 are explained below.
- Long Division Method
- Using Euclid's Algorithm
- Prime Factorization Method
GCF of 7 and 63 by Long Division
GCF of 7 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 7 (smaller number).
- Step 2: Since the remainder = 0, the divisor (7) is the GCF of 7 and 63.
The corresponding divisor (7) is the GCF of 7 and 63.
GCF of 7 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 = 7
- GCF(63, 7) = GCF(7, 63 mod 7) = GCF(7, 0)
- GCF(7, 0) = 7 (∵ GCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of GCF of 7 and 63 is 7.
GCF of 7 and 63 by Prime Factorization
Prime factorization of 7 and 63 is (7) and (3 × 3 × 7) respectively. As visible, 7 and 63 have only one common prime factor i.e. 7. Hence, the GCF of 7 and 63 is 7.
☛ Also Check:
- GCF of 20 and 24 = 4
- GCF of 6 and 15 = 3
- GCF of 15 and 27 = 3
- GCF of 33 and 66 = 33
- GCF of 12 and 54 = 6
- GCF of 51 and 85 = 17
- GCF of 49 and 63 = 7
FAQs on GCF of 7 and 63
What is the GCF of 7 and 63?
The GCF of 7 and 63 is 7. To calculate the greatest common factor (GCF) of 7 and 63, we need to factor each number (factors of 7 = 1, 7; factors of 63 = 1, 3, 7, 9, 21, 63) and choose the greatest factor that exactly divides both 7 and 63, i.e., 7.
How to Find the GCF of 7 and 63 by Prime Factorization?
To find the GCF of 7 and 63, we will find the prime factorization of the given numbers, i.e. 7 = 7; 63 = 3 × 3 × 7.
⇒ Since 7 is the only common prime factor of 7 and 63. Hence, GCF (7, 63) = 7.
☛ Prime Number
If the GCF of 63 and 7 is 7, Find its LCM.
GCF(63, 7) × LCM(63, 7) = 63 × 7
Since the GCF of 63 and 7 = 7
⇒ 7 × LCM(63, 7) = 441
Therefore, LCM = 63
☛ Greatest Common Factor Calculator
How to Find the GCF of 7 and 63 by Long Division Method?
To find the GCF of 7, 63 using long division method, 63 is divided by 7. The corresponding divisor (7) when remainder equals 0 is taken as GCF.
What are the Methods to Find GCF of 7 and 63?
There are three commonly used methods to find the GCF of 7 and 63.
- By Listing Common Factors
- By Prime Factorization
- By Long Division
What is the Relation Between LCM and GCF of 7, 63?
The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 7 and 63, i.e. GCF × LCM = 7 × 63.