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HCF of 56 and 84

HCF of 56 and 84 is the largest possible number that divides 56 and 84 exactly without any remainder. The factors of 56 and 84 are 1, 2, 4, 7, 8, 14, 28, 56 and 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 respectively. There are 3 commonly used methods to find the HCF of 56 and 84 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 56 and 84
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 56 and 84?

Answer: HCF of 56 and 84 is 28.

Explanation:

The HCF of two non-zero integers, x(56) and y(84), is the highest positive integer m(28) that divides both x(56) and y(84) without any remainder.

Methods to Find HCF of 56 and 84

Let's look at the different methods for finding the HCF of 56 and 84.

Long Division Method
Listing Common Factors
Using Euclid's Algorithm

HCF of 56 and 84 by Long Division

HCF of 56 and 84 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 84 (larger number) by 56 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (56) by the remainder (28).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (28) is the HCF of 56 and 84.

HCF of 56 and 84 by Listing Common Factors

Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

There are 6 common factors of 56 and 84, that are 1, 2, 4, 7, 14, and 28. Therefore, the highest common factor of 56 and 84 is 28.

HCF of 56 and 84 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 = 84 and Y = 56

HCF(84, 56) = HCF(56, 84 mod 56) = HCF(56, 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 56 and 84 is 28.

☛ Also Check:

HCF of 56 and 84 Examples

Example 1: Find the HCF of 56 and 84, if their LCM is 168.

Solution:

∵ LCM × HCF = 56 × 84
⇒ HCF(56, 84) = (56 × 84)/168 = 28
Therefore, the highest common factor of 56 and 84 is 28.
Example 2: The product of two numbers is 4704. If their HCF is 28, what is their LCM?

Solution:

Given: HCF = 28 and product of numbers = 4704
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 4704/28
Therefore, the LCM is 168.
Example 3: Find the highest number that divides 56 and 84 exactly.

Solution:

The highest number that divides 56 and 84 exactly is their highest common factor, i.e. HCF of 56 and 84.
⇒ Factors of 56 and 84:
- Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56
- Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Therefore, the HCF of 56 and 84 is 28.

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FAQs on HCF of 56 and 84

What is the HCF of 56 and 84?

The HCF of 56 and 84 is 28. To calculate the Highest common factor (HCF) of 56 and 84, we need to factor each number (factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56; factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84) and choose the highest factor that exactly divides both 56 and 84, i.e., 28.

How to Find the HCF of 56 and 84 by Prime Factorization?

To find the HCF of 56 and 84, we will find the prime factorization of the given numbers, i.e. 56 = 2 × 2 × 2 × 7; 84 = 2 × 2 × 3 × 7.
⇒ Since 2, 2, 7 are common terms in the prime factorization of 56 and 84. Hence, HCF(56, 84) = 2 × 2 × 7 = 28
☛ Prime Numbers

If the HCF of 84 and 56 is 28, Find its LCM.

HCF(84, 56) × LCM(84, 56) = 84 × 56
Since the HCF of 84 and 56 = 28
⇒ 28 × LCM(84, 56) = 4704
Therefore, LCM = 168
☛ Highest Common Factor Calculator

What is the Relation Between LCM and HCF of 56, 84?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 56 and 84, i.e. HCF × LCM = 56 × 84.

What are the Methods to Find HCF of 56 and 84?

There are three commonly used methods to find the HCF of 56 and 84.

By Long Division
By Prime Factorization
By Listing Common Factors

How to Find the HCF of 56 and 84 by Long Division Method?

To find the HCF of 56, 84 using long division method, 84 is divided by 56. The corresponding divisor (28) when remainder equals 0 is taken as HCF.

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