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HCF of 4 and 20

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

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

What is HCF of 4 and 20?

Answer: HCF of 4 and 20 is 4.

Explanation:

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

Methods to Find HCF of 4 and 20

Let's look at the different methods for finding the HCF of 4 and 20.

Using Euclid's Algorithm
Prime Factorization Method
Long Division Method

HCF of 4 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 = 4

HCF(20, 4) = HCF(4, 20 mod 4) = HCF(4, 0)
HCF(4, 0) = 4 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 4 and 20 is 4.

HCF of 4 and 20 by Prime Factorization

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

HCF of 4 and 20 by Long Division

HCF of 4 and 20 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 20 (larger number) by 4 (smaller number).
Step 2: Since the remainder = 0, the divisor (4) is the HCF of 4 and 20.

The corresponding divisor (4) is the HCF of 4 and 20.

☛ Also Check:

HCF of 4 and 20 Examples

Example 1: Find the highest number that divides 4 and 20 exactly.

Solution:

The highest number that divides 4 and 20 exactly is their highest common factor, i.e. HCF of 4 and 20.
⇒ Factors of 4 and 20:
- Factors of 4 = 1, 2, 4
- Factors of 20 = 1, 2, 4, 5, 10, 20
Therefore, the HCF of 4 and 20 is 4.
Example 2: The product of two numbers is 80. If their HCF is 4, what is their LCM?

Solution:

Given: HCF = 4 and product of numbers = 80
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 80/4
Therefore, the LCM is 20.
Example 3: For two numbers, HCF = 4 and LCM = 20. If one number is 20, find the other number.

Solution:

Given: HCF (y, 20) = 4 and LCM (y, 20) = 20
∵ HCF × LCM = 20 × (y)
⇒ y = (HCF × LCM)/20
⇒ y = (4 × 20)/20
⇒ y = 4
Therefore, the other number is 4.

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FAQs on HCF of 4 and 20

What is the HCF of 4 and 20?

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

What is the Relation Between LCM and HCF of 4, 20?

The following equation can be used to express the relation between Least Common Multiple and HCF of 4 and 20, i.e. HCF × LCM = 4 × 20.

How to Find the HCF of 4 and 20 by Long Division Method?

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

How to Find the HCF of 4 and 20 by Prime Factorization?

To find the HCF of 4 and 20, we will find the prime factorization of the given numbers, i.e. 4 = 2 × 2; 20 = 2 × 2 × 5.
⇒ Since 2, 2 are common terms in the prime factorization of 4 and 20. Hence, HCF(4, 20) = 2 × 2 = 4
☛ Prime Number

What are the Methods to Find HCF of 4 and 20?

There are three commonly used methods to find the HCF of 4 and 20.

By Prime Factorization
By Long Division
By Euclidean Algorithm

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

HCF(20, 4) × LCM(20, 4) = 20 × 4
Since the HCF of 20 and 4 = 4
⇒ 4 × LCM(20, 4) = 80
Therefore, LCM = 20
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