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 nonzero 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.
☛ Also Check:
 HCF of 24 and 36 = 12
 HCF of 210 and 55 = 5
 HCF of 1 and 2 = 1
 HCF of 49 and 56 = 7
 HCF of 84 and 120 = 12
 HCF of 36 and 144 = 36
 HCF of 72 and 84 = 12
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.
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
☛ HCF Calculator
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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