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HCF of 12 and 18

HCF of 12 and 18 is the largest possible number that divides 12 and 18 exactly without any remainder. The factors of 12 and 18 are 1, 2, 3, 4, 6, 12 and 1, 2, 3, 6, 9, 18 respectively. There are 3 commonly used methods to find the HCF of 12 and 18 - long division, Euclidean algorithm, and prime factorization.

1.	HCF of 12 and 18
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 12 and 18?

Answer: HCF of 12 and 18 is 6.

Explanation:

The HCF of two non-zero integers, x(12) and y(18), is the highest positive integer m(6) that divides both x(12) and y(18) without any remainder.

Methods to Find HCF of 12 and 18

Let's look at the different methods for finding the HCF of 12 and 18.

Prime Factorization Method
Long Division Method
Listing Common Factors

HCF of 12 and 18 by Prime Factorization

Prime factorization of 12 and 18 is (2 × 2 × 3) and (2 × 3 × 3) respectively. As visible, 12 and 18 have common prime factors. Hence, the HCF of 12 and 18 is 2 × 3 = 6.

HCF of 12 and 18 by Long Division

HCF of 12 and 18 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 18 (larger number) by 12 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (12) by the remainder (6).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (6) is the HCF of 12 and 18.

HCF of 12 and 18 by Listing Common Factors

Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 18: 1, 2, 3, 6, 9, 18

There are 4 common factors of 12 and 18, that are 1, 2, 3, and 6. Therefore, the highest common factor of 12 and 18 is 6.

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HCF of 12 and 18 Examples

Example 1: For two numbers, HCF = 6 and LCM = 36. If one number is 12, find the other number.

Solution:

Given: HCF (y, 12) = 6 and LCM (y, 12) = 36
∵ HCF × LCM = 12 × (y)
⇒ y = (HCF × LCM)/12
⇒ y = (6 × 36)/12
⇒ y = 18
Therefore, the other number is 18.
Example 2: Find the highest number that divides 12 and 18 exactly.

Solution:

The highest number that divides 12 and 18 exactly is their highest common factor, i.e. HCF of 12 and 18.
⇒ Factors of 12 and 18:
- Factors of 12 = 1, 2, 3, 4, 6, 12
- Factors of 18 = 1, 2, 3, 6, 9, 18
Therefore, the HCF of 12 and 18 is 6.
Example 3: Find the HCF of 12 and 18, if their LCM is 36.

Solution:

∵ LCM × HCF = 12 × 18
⇒ HCF(12, 18) = (12 × 18)/36 = 6
Therefore, the highest common factor of 12 and 18 is 6.

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FAQs on HCF of 12 and 18

What is the HCF of 12 and 18?

The HCF of 12 and 18 is 6. To calculate the Highest common factor of 12 and 18, we need to factor each number (factors of 12 = 1, 2, 3, 4, 6, 12; factors of 18 = 1, 2, 3, 6, 9, 18) and choose the highest factor that exactly divides both 12 and 18, i.e., 6.

What is the Relation Between LCM and HCF of 12, 18?

The following equation can be used to express the relation between Least Common Multiple and HCF of 12 and 18, i.e. HCF × LCM = 12 × 18.

What are the Methods to Find HCF of 12 and 18?

There are three commonly used methods to find the HCF of 12 and 18.

By Long Division
By Listing Common Factors
By Prime Factorization

If the HCF of 18 and 12 is 6, Find its LCM.

HCF(18, 12) × LCM(18, 12) = 18 × 12
Since the HCF of 18 and 12 = 6
⇒ 6 × LCM(18, 12) = 216
Therefore, LCM = 36
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How to Find the HCF of 12 and 18 by Long Division Method?

To find the HCF of 12, 18 using long division method, 18 is divided by 12. The corresponding divisor (6) when remainder equals 0 is taken as HCF.

How to Find the HCF of 12 and 18 by Prime Factorization?

To find the HCF of 12 and 18, we will find the prime factorization of the given numbers, i.e. 12 = 2 × 2 × 3; 18 = 2 × 3 × 3.
⇒ Since 2, 3 are common terms in the prime factorization of 12 and 18. Hence, HCF(12, 18) = 2 × 3 = 6
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