The HCF of 20 and 48 is 4. The Highest Common Factor (HCF) of two numbers is defined as the highest factor that divides the given two numbers exactly, without leaving any remainder. Prime factorisation, long division method and listing common factors are the frequently used methods to find the HCF of given numbers. Students who get stuck while solving problems based on HCF can make use of the article HCF as the best study material to clear their doubts and grasp the concept effortlessly. Here, we will learn the simple procedure on how to find the Highest Common Factor of 20 and 48 in a comprehensive manner.
What is the HCF of 20 and 48?
The Highest Common Factor of 20 and 48 is 4. This article offers a clear explanation of how to calculate the HCF of 20 and 48 with the help of simple steps.
How to Find HCF of 20 and 48?
There are three methods to find the HCF of 20 and 48:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 20 and 48 by Prime Factorisation Method
To find the HCF by the prime factorisation method, given numbers are written as the product of prime factors. Therefore, the numbers 20 and 48 can be expressed as:
20 = 2 × 2 × 5
48 = 2 × 2 × 2 × 2 × 3
Common prime factors of 20 and 48 are 2 and 2
Therefore, HCF (20, 48) = 2 × 2 = 4
HCF of 20 and 48 by Long Division Method
In the long division method, we can go through the steps mentioned below to find the HCF of 20 and 48:
Step 1: Divide the largest number by the smallest number from the given two numbers.
Step 2: Now, check the remainder. If it is not 0, then make it a new divisor and write the previous divisor as the new dividend. Then perform the division.
Step 3: Repeat this process until we get the remainder as zero. The last divisor will be considered as the HCF of the given two numbers.
The HCF of 20 and 48 by long division method is:
Hence, HCF (20, 48) = 4
HCF of 20 and 48 by Listing Common Factors
In this method, we can find the HCF of 20 and 48 by listing out their factors. The factors of 20 and 48 are as follows:
Factors of 20:1, 2, 4, 5, 10, 20
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Hence, HCF (20, 48) = 4
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Solved Examples
1. What is the highest number that divides both 20 and 48 exactly?
Solution: The highest number that divides both 20 and 48 exactly is their Highest Common Factor. To find the HCF, let us list the 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
Here, 4 is the Highest Common Factor of 20 and 48. Hence, the highest number that divides both 20 and 48 is 4.
2. What is the HCF of 20 and 48 if their LCM is 240?
Solution: Given
LCM = 240
We know that
LCM × HCF = 20 × 48
HCF = (20 × 48)/LCM
HCF = (20 × 48)/240
HCF = 960/240 = 4
Hence, the HCF of 20 and 48 is 4.
Frequently Asked Questions on HCF of 20 and 48
What is the HCF of 20 and 48?
How to find the HCF of 20 and 48 by prime factorisation?
In the prime factorisation method, we can express the given numbers as the product of prime factors. Therefore the numbers 20 and 48 can be expressed as:
20 = 2 × 2 × 5
48 = 2 × 2 × 2 × 2 × 3
Common prime factors of 20 and 48 are 2 and 2
Therefore, HCF (20, 48) = 2 × 2 = 4
Name the methods to find the HCF of 20 and 48.
The methods used to find the HCF of 20 and 48 are as follows:
Prime Factorisation
Long Division method
Listing common factors
What is the LCM if the HCF of 20 and 48 is 4?
We know that
HCF × LCM = 20 × 48
Given
HCF = 4
4 × LCM = 20 × 48
LCM = 960/4 = 240
Hence, the LCM is 240.
Write the relation between LCM and HCF of 20 and 48.
The below equation is used to express the relation between LCM and HCF of 20 and 48
HCF × LCM = 20 × 48 = 960
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