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HCF of 12 and 56

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

1.	HCF of 12 and 56
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 12 and 56?

Answer: HCF of 12 and 56 is 4.

Explanation:

The HCF of two non-zero integers, x(12) and y(56), is the highest positive integer m(4) that divides both x(12) and y(56) without any remainder.

Methods to Find HCF of 12 and 56

Let's look at the different methods for finding the HCF of 12 and 56.

Long Division Method
Listing Common Factors
Using Euclid's Algorithm

HCF of 12 and 56 by Long Division

HCF of 12 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 12 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (12) by the remainder (8).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the HCF of 12 and 56.

HCF of 12 and 56 by Listing Common Factors

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

There are 3 common factors of 12 and 56, that are 1, 2, and 4. Therefore, the highest common factor of 12 and 56 is 4.

HCF of 12 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 = 12

HCF(56, 12) = HCF(12, 56 mod 12) = HCF(12, 8)
HCF(12, 8) = HCF(8, 12 mod 8) = HCF(8, 4)
HCF(8, 4) = HCF(4, 8 mod 4) = HCF(4, 0)
HCF(4, 0) = 4 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 12 and 56 is 4.

☛ Also Check:

HCF of 12 and 56 Examples

Example 1: The product of two numbers is 672. If their HCF is 4, what is their LCM?

Solution:

Given: HCF = 4 and product of numbers = 672
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 672/4
Therefore, the LCM is 168.
Example 2: For two numbers, HCF = 4 and LCM = 168. If one number is 12, find the other number.

Solution:

Given: HCF (y, 12) = 4 and LCM (y, 12) = 168
∵ HCF × LCM = 12 × (y)
⇒ y = (HCF × LCM)/12
⇒ y = (4 × 168)/12
⇒ y = 56
Therefore, the other number is 56.
Example 3: Find the highest number that divides 12 and 56 exactly.

Solution:

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

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FAQs on HCF of 12 and 56

What is the HCF of 12 and 56?

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

What is the Relation Between LCM and HCF of 12, 56?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 12 and 56, i.e. HCF × LCM = 12 × 56.

How to Find the HCF of 12 and 56 by Prime Factorization?

To find the HCF of 12 and 56, we will find the prime factorization of the given numbers, i.e. 12 = 2 × 2 × 3; 56 = 2 × 2 × 2 × 7.
⇒ Since 2, 2 are common terms in the prime factorization of 12 and 56. Hence, HCF(12, 56) = 2 × 2 = 4
☛ What are Prime Numbers?

If the HCF of 56 and 12 is 4, Find its LCM.

HCF(56, 12) × LCM(56, 12) = 56 × 12
Since the HCF of 56 and 12 = 4
⇒ 4 × LCM(56, 12) = 672
Therefore, LCM = 168
☛ Highest Common Factor Calculator

How to Find the HCF of 12 and 56 by Long Division Method?

To find the HCF of 12, 56 using long division method, 56 is divided by 12. The corresponding divisor (4) when remainder equals 0 is taken as HCF.

What are the Methods to Find HCF of 12 and 56?

There are three commonly used methods to find the HCF of 12 and 56.

By Prime Factorization
By Listing Common Factors
By Long Division

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