HCF of 49 and 56
HCF of 49 and 56 is the largest possible number that divides 49 and 56 exactly without any remainder. The factors of 49 and 56 are 1, 7, 49 and 1, 2, 4, 7, 8, 14, 28, 56 respectively. There are 3 commonly used methods to find the HCF of 49 and 56 - Euclidean algorithm, prime factorization, and long division.
| 1. | HCF of 49 and 56 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is HCF of 49 and 56?
Answer: HCF of 49 and 56 is 7.
Explanation:
The HCF of two non-zero integers, x(49) and y(56), is the highest positive integer m(7) that divides both x(49) and y(56) without any remainder.
Methods to Find HCF of 49 and 56
Let's look at the different methods for finding the HCF of 49 and 56.
- Using Euclid's Algorithm
- Long Division Method
- Prime Factorization Method
HCF of 49 and 56 by Euclidean Algorithm
As per the Euclidean Algorithm, HCF(X, Y) = HCF(Y, X mod Y)
where X > Y and mod is the modulo operator.
Here X = 56 and Y = 49
- HCF(56, 49) = HCF(49, 56 mod 49) = HCF(49, 7)
- HCF(49, 7) = HCF(7, 49 mod 7) = HCF(7, 0)
- HCF(7, 0) = 7 (∵ HCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of HCF of 49 and 56 is 7.
HCF of 49 and 56 by Long Division
HCF of 49 and 56 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 HCF of 49 and 56.
HCF of 49 and 56 by Prime Factorization
Prime factorization of 49 and 56 is (7 × 7) and (2 × 2 × 2 × 7) respectively. As visible, 49 and 56 have only one common prime factor i.e. 7. Hence, the HCF of 49 and 56 is 7.
☛ Also Check:
- HCF of 8, 10 and 12 = 2
- HCF of 1 and 2 = 1
- HCF of 100 and 190 = 10
- HCF of 52 and 117 = 13
- HCF of 12 and 30 = 6
- HCF of 36 and 42 = 6
- HCF of 18 and 20 = 2
FAQs on HCF of 49 and 56
What is the HCF of 49 and 56?
The HCF of 49 and 56 is 7. To calculate the Highest common factor of 49 and 56, we need to factor each number (factors of 49 = 1, 7, 49; factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56) and choose the highest factor that exactly divides both 49 and 56, i.e., 7.
What is the Relation Between LCM and HCF of 49, 56?
The following equation can be used to express the relation between LCM and HCF of 49 and 56, i.e. HCF × LCM = 49 × 56.
How to Find the HCF of 49 and 56 by Prime Factorization?
To find the HCF of 49 and 56, we will find the prime factorization of the given numbers, i.e. 49 = 7 × 7; 56 = 2 × 2 × 2 × 7.
⇒ Since 7 is the only common prime factor of 49 and 56. Hence, HCF (49, 56) = 7.
☛ What are Prime Numbers?
What are the Methods to Find HCF of 49 and 56?
There are three commonly used methods to find the HCF of 49 and 56.
- By Long Division
- By Euclidean Algorithm
- By Prime Factorization
How to Find the HCF of 49 and 56 by Long Division Method?
To find the HCF of 49, 56 using long division method, 56 is divided by 49. The corresponding divisor (7) when remainder equals 0 is taken as HCF.
If the HCF of 56 and 49 is 7, Find its LCM.
HCF(56, 49) × LCM(56, 49) = 56 × 49
Since the HCF of 56 and 49 = 7
⇒ 7 × LCM(56, 49) = 2744
Therefore, LCM = 392
☛ Highest Common Factor Calculator