A day full of math games & activities. Find one near you.

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 non-zero 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 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.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

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
☛ Highest Common Factor Calculator

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
☛ Prime Numbers

Download FREE Study Materials

HCF and LCM

Math worksheets and
visual curriculum