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HCF of 12 and 20

HCF of 12 and 20 is the largest possible number that divides 12 and 20 exactly without any remainder. The factors of 12 and 20 are 1, 2, 3, 4, 6, 12 and 1, 2, 4, 5, 10, 20 respectively. There are 3 commonly used methods to find the HCF of 12 and 20 - long division, prime factorization, and Euclidean algorithm.

1.	HCF of 12 and 20
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 12 and 20?

Answer: HCF of 12 and 20 is 4.

Explanation:

The HCF of two non-zero integers, x(12) and y(20), is the highest positive integer m(4) that divides both x(12) and y(20) without any remainder.

Methods to Find HCF of 12 and 20

Let's look at the different methods for finding the HCF of 12 and 20.

Using Euclid's Algorithm
Listing Common Factors
Prime Factorization Method

HCF of 12 and 20 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 = 20 and Y = 12

HCF(20, 12) = HCF(12, 20 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 20 is 4.

HCF of 12 and 20 by Listing Common Factors

Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 20: 1, 2, 4, 5, 10, 20

There are 3 common factors of 12 and 20, that are 1, 2, and 4. Therefore, the highest common factor of 12 and 20 is 4.

HCF of 12 and 20 by Prime Factorization

Prime factorization of 12 and 20 is (2 × 2 × 3) and (2 × 2 × 5) respectively. As visible, 12 and 20 have common prime factors. Hence, the HCF of 12 and 20 is 2 × 2 = 4.

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HCF of 12 and 20 Examples

Example 1: For two numbers, HCF = 4 and LCM = 60. If one number is 20, find the other number.

Solution:

Given: HCF (z, 20) = 4 and LCM (z, 20) = 60
∵ HCF × LCM = 20 × (z)
⇒ z = (HCF × LCM)/20
⇒ z = (4 × 60)/20
⇒ z = 12
Therefore, the other number is 12.
Example 2: Find the highest number that divides 12 and 20 exactly.

Solution:

The highest number that divides 12 and 20 exactly is their highest common factor, i.e. HCF of 12 and 20.
⇒ Factors of 12 and 20:
- Factors of 12 = 1, 2, 3, 4, 6, 12
- Factors of 20 = 1, 2, 4, 5, 10, 20
Therefore, the HCF of 12 and 20 is 4.
Example 3: The product of two numbers is 240. If their HCF is 4, what is their LCM?

Solution:

Given: HCF = 4 and product of numbers = 240
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 240/4
Therefore, the LCM is 60.

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FAQs on HCF of 12 and 20

What is the HCF of 12 and 20?

The HCF of 12 and 20 is 4. To calculate the HCF (Highest Common Factor) of 12 and 20, we need to factor each number (factors of 12 = 1, 2, 3, 4, 6, 12; factors of 20 = 1, 2, 4, 5, 10, 20) and choose the highest factor that exactly divides both 12 and 20, i.e., 4.

How to Find the HCF of 12 and 20 by Long Division Method?

To find the HCF of 12, 20 using long division method, 20 is divided by 12. The corresponding divisor (4) when remainder equals 0 is taken as HCF.

If the HCF of 20 and 12 is 4, Find its LCM.

HCF(20, 12) × LCM(20, 12) = 20 × 12
Since the HCF of 20 and 12 = 4
⇒ 4 × LCM(20, 12) = 240
Therefore, LCM = 60
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What are the Methods to Find HCF of 12 and 20?

There are three commonly used methods to find the HCF of 12 and 20.

By Listing Common Factors
By Prime Factorization
By Long Division

How to Find the HCF of 12 and 20 by Prime Factorization?

To find the HCF of 12 and 20, we will find the prime factorization of the given numbers, i.e. 12 = 2 × 2 × 3; 20 = 2 × 2 × 5.
⇒ Since 2, 2 are common terms in the prime factorization of 12 and 20. Hence, HCF(12, 20) = 2 × 2 = 4
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What is the Relation Between LCM and HCF of 12, 20?

The following equation can be used to express the relation between Least Common Multiple and HCF of 12 and 20, i.e. HCF × LCM = 12 × 20.

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