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HCF of 20 and 48

HCF of 20 and 48 is the largest possible number that divides 20 and 48 exactly without any remainder. The factors of 20 and 48 are 1, 2, 4, 5, 10, 20 and 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 respectively. There are 3 commonly used methods to find the HCF of 20 and 48 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 20 and 48
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 20 and 48?

Answer: HCF of 20 and 48 is 4.

Explanation:

The HCF of two non-zero integers, x(20) and y(48), is the highest positive integer m(4) that divides both x(20) and y(48) without any remainder.

Methods to Find HCF of 20 and 48

The methods to find the HCF of 20 and 48 are explained below.

Listing Common Factors
Long Division Method
Using Euclid's Algorithm

HCF of 20 and 48 by Listing Common Factors

Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

There are 3 common factors of 20 and 48, that are 1, 2, and 4. Therefore, the highest common factor of 20 and 48 is 4.

HCF of 20 and 48 by Long Division

HCF of 20 and 48 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 48 (larger number) by 20 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (20) by the remainder (8).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the HCF of 20 and 48.

HCF of 20 and 48 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 = 48 and Y = 20

HCF(48, 20) = HCF(20, 48 mod 20) = HCF(20, 8)
HCF(20, 8) = HCF(8, 20 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 20 and 48 is 4.

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HCF of 20 and 48 Examples

Example 1: Find the HCF of 20 and 48, if their LCM is 240.

Solution:

∵ LCM × HCF = 20 × 48
⇒ HCF(20, 48) = (20 × 48)/240 = 4
Therefore, the highest common factor of 20 and 48 is 4.
Example 2: Find the highest number that divides 20 and 48 exactly.

Solution:

The highest number that divides 20 and 48 exactly is their highest common factor, i.e. HCF of 20 and 48.
⇒ Factors of 20 and 48:
- Factors of 20 = 1, 2, 4, 5, 10, 20
- Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Therefore, the HCF of 20 and 48 is 4.
Example 3: For two numbers, HCF = 4 and LCM = 240. If one number is 20, find the other number.

Solution:

Given: HCF (z, 20) = 4 and LCM (z, 20) = 240
∵ HCF × LCM = 20 × (z)
⇒ z = (HCF × LCM)/20
⇒ z = (4 × 240)/20
⇒ z = 48
Therefore, the other number is 48.

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FAQs on HCF of 20 and 48

What is the HCF of 20 and 48?

The HCF of 20 and 48 is 4. To calculate the HCF of 20 and 48, we need to factor each number (factors of 20 = 1, 2, 4, 5, 10, 20; factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48) and choose the highest factor that exactly divides both 20 and 48, i.e., 4.

If the HCF of 48 and 20 is 4, Find its LCM.

HCF(48, 20) × LCM(48, 20) = 48 × 20
Since the HCF of 48 and 20 = 4
⇒ 4 × LCM(48, 20) = 960
Therefore, LCM = 240
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What is the Relation Between LCM and HCF of 20, 48?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 20 and 48, i.e. HCF × LCM = 20 × 48.

How to Find the HCF of 20 and 48 by Long Division Method?

To find the HCF of 20, 48 using long division method, 48 is divided by 20. The corresponding divisor (4) when remainder equals 0 is taken as HCF.

How to Find the HCF of 20 and 48 by Prime Factorization?

To find the HCF of 20 and 48, we will find the prime factorization of the given numbers, i.e. 20 = 2 × 2 × 5; 48 = 2 × 2 × 2 × 2 × 3.
⇒ Since 2, 2 are common terms in the prime factorization of 20 and 48. Hence, HCF(20, 48) = 2 × 2 = 4
☛ What are Prime Numbers?

What are the Methods to Find HCF of 20 and 48?

There are three commonly used methods to find the HCF of 20 and 48.

By Long Division
By Prime Factorization
By Listing Common Factors

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