HCF of 28 and 56
HCF of 28 and 56 is the largest possible number that divides 28 and 56 exactly without any remainder. The factors of 28 and 56 are 1, 2, 4, 7, 14, 28 and 1, 2, 4, 7, 8, 14, 28, 56 respectively. There are 3 commonly used methods to find the HCF of 28 and 56  Euclidean algorithm, prime factorization, and long division.
1.  HCF of 28 and 56 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is HCF of 28 and 56?
Answer: HCF of 28 and 56 is 28.
Explanation:
The HCF of two nonzero integers, x(28) and y(56), is the highest positive integer m(28) that divides both x(28) and y(56) without any remainder.
Methods to Find HCF of 28 and 56
The methods to find the HCF of 28 and 56 are explained below.
 Long Division Method
 Prime Factorization Method
 Using Euclid's Algorithm
HCF of 28 and 56 by Long Division
HCF of 28 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 28 (smaller number).
 Step 2: Since the remainder = 0, the divisor (28) is the HCF of 28 and 56.
The corresponding divisor (28) is the HCF of 28 and 56.
HCF of 28 and 56 by Prime Factorization
Prime factorization of 28 and 56 is (2 × 2 × 7) and (2 × 2 × 2 × 7) respectively. As visible, 28 and 56 have common prime factors. Hence, the HCF of 28 and 56 is 2 × 2 × 7 = 28.
HCF of 28 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 = 28
 HCF(56, 28) = HCF(28, 56 mod 28) = HCF(28, 0)
 HCF(28, 0) = 28 (∵ HCF(X, 0) = X, where X ≠ 0)
Therefore, the value of HCF of 28 and 56 is 28.
☛ Also Check:
 HCF of 825, 675 and 450 = 75
 HCF of 126 and 156 = 6
 HCF of 35 and 40 = 5
 HCF of 408 and 1032 = 24
 HCF of 12 and 36 = 12
 HCF of 6 and 8 = 2
 HCF of 56, 96 and 404 = 4
HCF of 28 and 56 Examples

Example 1: For two numbers, HCF = 28 and LCM = 56. If one number is 28, find the other number.
Solution:
Given: HCF (z, 28) = 28 and LCM (z, 28) = 56
∵ HCF × LCM = 28 × (z)
⇒ z = (HCF × LCM)/28
⇒ z = (28 × 56)/28
⇒ z = 56
Therefore, the other number is 56. 
Example 2: The product of two numbers is 1568. If their HCF is 28, what is their LCM?
Solution:
Given: HCF = 28 and product of numbers = 1568
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 1568/28
Therefore, the LCM is 56. 
Example 3: Find the HCF of 28 and 56, if their LCM is 56.
Solution:
∵ LCM × HCF = 28 × 56
⇒ HCF(28, 56) = (28 × 56)/56 = 28
Therefore, the highest common factor of 28 and 56 is 28.
FAQs on HCF of 28 and 56
What is the HCF of 28 and 56?
The HCF of 28 and 56 is 28. To calculate the HCF of 28 and 56, we need to factor each number (factors of 28 = 1, 2, 4, 7, 14, 28; factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56) and choose the highest factor that exactly divides both 28 and 56, i.e., 28.
How to Find the HCF of 28 and 56 by Long Division Method?
To find the HCF of 28, 56 using long division method, 56 is divided by 28. The corresponding divisor (28) when remainder equals 0 is taken as HCF.
What are the Methods to Find HCF of 28 and 56?
There are three commonly used methods to find the HCF of 28 and 56.
 By Euclidean Algorithm
 By Long Division
 By Prime Factorization
What is the Relation Between LCM and HCF of 28, 56?
The following equation can be used to express the relation between Least Common Multiple and HCF of 28 and 56, i.e. HCF × LCM = 28 × 56.
If the HCF of 56 and 28 is 28, Find its LCM.
HCF(56, 28) × LCM(56, 28) = 56 × 28
Since the HCF of 56 and 28 = 28
⇒ 28 × LCM(56, 28) = 1568
Therefore, LCM = 56
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How to Find the HCF of 28 and 56 by Prime Factorization?
To find the HCF of 28 and 56, we will find the prime factorization of the given numbers, i.e. 28 = 2 × 2 × 7; 56 = 2 × 2 × 2 × 7.
⇒ Since 2, 2, 7 are common terms in the prime factorization of 28 and 56. Hence, HCF(28, 56) = 2 × 2 × 7 = 28
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