GCF of 56 and 49
GCF of 56 and 49 is the largest possible number that divides 56 and 49 exactly without any remainder. The factors of 56 and 49 are 1, 2, 4, 7, 8, 14, 28, 56 and 1, 7, 49 respectively. There are 3 commonly used methods to find the GCF of 56 and 49 - prime factorization, Euclidean algorithm, and long division.
| 1. | GCF of 56 and 49 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 56 and 49?
Answer: GCF of 56 and 49 is 7.
Explanation:
The GCF of two non-zero integers, x(56) and y(49), is the greatest positive integer m(7) that divides both x(56) and y(49) without any remainder.
Methods to Find GCF of 56 and 49
The methods to find the GCF of 56 and 49 are explained below.
- Long Division Method
- Prime Factorization Method
- Listing Common Factors
GCF of 56 and 49 by Long Division
GCF of 56 and 49 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 56 (larger number) by 49 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (49) by the remainder (7).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (7) is the GCF of 56 and 49.
GCF of 56 and 49 by Prime Factorization
Prime factorization of 56 and 49 is (2 × 2 × 2 × 7) and (7 × 7) respectively. As visible, 56 and 49 have only one common prime factor i.e. 7. Hence, the GCF of 56 and 49 is 7.
GCF of 56 and 49 by Listing Common Factors
- Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
- Factors of 49: 1, 7, 49
There are 2 common factors of 56 and 49, that are 1 and 7. Therefore, the greatest common factor of 56 and 49 is 7.
☛ Also Check:
- GCF of 16 and 48 = 16
- GCF of 75 and 90 = 15
- GCF of 54 and 27 = 27
- GCF of 12 and 15 = 3
- GCF of 30 and 75 = 15
- GCF of 18 and 45 = 9
- GCF of 8 and 18 = 2
FAQs on GCF of 56 and 49
What is the GCF of 56 and 49?
The GCF of 56 and 49 is 7. To calculate the greatest common factor (GCF) of 56 and 49, we need to factor each number (factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56; factors of 49 = 1, 7, 49) and choose the greatest factor that exactly divides both 56 and 49, i.e., 7.
How to Find the GCF of 56 and 49 by Prime Factorization?
To find the GCF of 56 and 49, we will find the prime factorization of the given numbers, i.e. 56 = 2 × 2 × 2 × 7; 49 = 7 × 7.
⇒ Since 7 is the only common prime factor of 56 and 49. Hence, GCF (56, 49) = 7.
☛ Prime Numbers
How to Find the GCF of 56 and 49 by Long Division Method?
To find the GCF of 56, 49 using long division method, 56 is divided by 49. The corresponding divisor (7) when remainder equals 0 is taken as GCF.
If the GCF of 49 and 56 is 7, Find its LCM.
GCF(49, 56) × LCM(49, 56) = 49 × 56
Since the GCF of 49 and 56 = 7
⇒ 7 × LCM(49, 56) = 2744
Therefore, LCM = 392
☛ Greatest Common Factor Calculator
What is the Relation Between LCM and GCF of 56, 49?
The following equation can be used to express the relation between Least Common Multiple and GCF of 56 and 49, i.e. GCF × LCM = 56 × 49.
What are the Methods to Find GCF of 56 and 49?
There are three commonly used methods to find the GCF of 56 and 49.
- By Prime Factorization
- By Euclidean Algorithm
- By Long Division