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HCF of 8 and 12

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

1.	HCF of 8 and 12
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 8 and 12?

Answer: HCF of 8 and 12 is 4.

Explanation:

The HCF of two non-zero integers, x(8) and y(12), is the highest positive integer m(4) that divides both x(8) and y(12) without any remainder.

Methods to Find HCF of 8 and 12

Let's look at the different methods for finding the HCF of 8 and 12.

Using Euclid's Algorithm
Long Division Method
Prime Factorization Method

HCF of 8 and 12 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 = 12 and Y = 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 8 and 12 is 4.

HCF of 8 and 12 by Long Division

HCF of 8 and 12 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 12 (larger number) by 8 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (8) by the remainder (4).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the HCF of 8 and 12.

HCF of 8 and 12 by Prime Factorization

Prime factorization of 8 and 12 is (2 × 2 × 2) and (2 × 2 × 3) respectively. As visible, 8 and 12 have common prime factors. Hence, the HCF of 8 and 12 is 2 × 2 = 4.

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HCF of 8 and 12 Examples

Example 1: Find the highest number that divides 8 and 12 exactly.

Solution:

The highest number that divides 8 and 12 exactly is their highest common factor, i.e. HCF of 8 and 12.
⇒ Factors of 8 and 12:
- Factors of 8 = 1, 2, 4, 8
- Factors of 12 = 1, 2, 3, 4, 6, 12
Therefore, the HCF of 8 and 12 is 4.
Example 2: Find the HCF of 8 and 12, if their LCM is 24.

Solution:

∵ LCM × HCF = 8 × 12
⇒ HCF(8, 12) = (8 × 12)/24 = 4
Therefore, the highest common factor of 8 and 12 is 4.
Example 3: For two numbers, HCF = 4 and LCM = 24. If one number is 8, find the other number.

Solution:

Given: HCF (y, 8) = 4 and LCM (y, 8) = 24
∵ HCF × LCM = 8 × (y)
⇒ y = (HCF × LCM)/8
⇒ y = (4 × 24)/8
⇒ y = 12
Therefore, the other number is 12.

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FAQs on HCF of 8 and 12

What is the HCF of 8 and 12?

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

How to Find the HCF of 8 and 12 by Prime Factorization?

To find the HCF of 8 and 12, we will find the prime factorization of the given numbers, i.e. 8 = 2 × 2 × 2; 12 = 2 × 2 × 3.
⇒ Since 2, 2 are common terms in the prime factorization of 8 and 12. Hence, HCF(8, 12) = 2 × 2 = 4
☛ What are Prime Numbers?

What are the Methods to Find HCF of 8 and 12?

There are three commonly used methods to find the HCF of 8 and 12.

By Prime Factorization
By Long Division
By Listing Common Factors

What is the Relation Between LCM and HCF of 8, 12?

The following equation can be used to express the relation between LCM and HCF of 8 and 12, i.e. HCF × LCM = 8 × 12.

How to Find the HCF of 8 and 12 by Long Division Method?

To find the HCF of 8, 12 using long division method, 12 is divided by 8. The corresponding divisor (4) when remainder equals 0 is taken as HCF.

If the HCF of 12 and 8 is 4, Find its LCM.

HCF(12, 8) × LCM(12, 8) = 12 × 8
Since the HCF of 12 and 8 = 4
⇒ 4 × LCM(12, 8) = 96
Therefore, LCM = 24
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