GCF of 56 and 63
GCF of 56 and 63 is the largest possible number that divides 56 and 63 exactly without any remainder. The factors of 56 and 63 are 1, 2, 4, 7, 8, 14, 28, 56 and 1, 3, 7, 9, 21, 63 respectively. There are 3 commonly used methods to find the GCF of 56 and 63 - long division, Euclidean algorithm, and prime factorization.
| 1. | GCF of 56 and 63 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 56 and 63?
Answer: GCF of 56 and 63 is 7.
Explanation:
The GCF of two non-zero integers, x(56) and y(63), is the greatest positive integer m(7) that divides both x(56) and y(63) without any remainder.
Methods to Find GCF of 56 and 63
Let's look at the different methods for finding the GCF of 56 and 63.
- Prime Factorization Method
- Long Division Method
- Using Euclid's Algorithm
GCF of 56 and 63 by Prime Factorization
Prime factorization of 56 and 63 is (2 × 2 × 2 × 7) and (3 × 3 × 7) respectively. As visible, 56 and 63 have only one common prime factor i.e. 7. Hence, the GCF of 56 and 63 is 7.
GCF of 56 and 63 by Long Division
GCF of 56 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 56 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (56) by the remainder (7).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (7) is the GCF of 56 and 63.
GCF of 56 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 = 56
- GCF(63, 56) = GCF(56, 63 mod 56) = GCF(56, 7)
- GCF(56, 7) = GCF(7, 56 mod 7) = GCF(7, 0)
- GCF(7, 0) = 7 (∵ GCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of GCF of 56 and 63 is 7.
☛ Also Check:
- GCF of 42 and 56 = 14
- GCF of 15 and 64 = 1
- GCF of 5 and 30 = 5
- GCF of 68 and 102 = 34
- GCF of 20 and 100 = 20
- GCF of 30 and 54 = 6
- GCF of 12 and 36 = 12
FAQs on GCF of 56 and 63
What is the GCF of 56 and 63?
The GCF of 56 and 63 is 7. To calculate the greatest common factor of 56 and 63, we need to factor each number (factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56; factors of 63 = 1, 3, 7, 9, 21, 63) and choose the greatest factor that exactly divides both 56 and 63, i.e., 7.
How to Find the GCF of 56 and 63 by Long Division Method?
To find the GCF of 56, 63 using long division method, 63 is divided by 56. The corresponding divisor (7) when remainder equals 0 is taken as GCF.
How to Find the GCF of 56 and 63 by Prime Factorization?
To find the GCF of 56 and 63, we will find the prime factorization of the given numbers, i.e. 56 = 2 × 2 × 2 × 7; 63 = 3 × 3 × 7.
⇒ Since 7 is the only common prime factor of 56 and 63. Hence, GCF (56, 63) = 7.
☛ What is a Prime Number?
If the GCF of 63 and 56 is 7, Find its LCM.
GCF(63, 56) × LCM(63, 56) = 63 × 56
Since the GCF of 63 and 56 = 7
⇒ 7 × LCM(63, 56) = 3528
Therefore, LCM = 504
☛ GCF Calculator
What are the Methods to Find GCF of 56 and 63?
There are three commonly used methods to find the GCF of 56 and 63.
- By Prime Factorization
- By Listing Common Factors
- By Long Division
What is the Relation Between LCM and GCF of 56, 63?
The following equation can be used to express the relation between Least Common Multiple and GCF of 56 and 63, i.e. GCF × LCM = 56 × 63.