The HCF of 12 and 20 is 4. The factors of 12 and 20 are 1, 2, 3, 4, 6, 12 and 1, 2, 4, 5, 10, 20, respectively. Here, 4 is the largest number present in both the factors of 12 and 20. Hence, the number that divides both 12 and 20 exactly is 4. Therefore, the Highest Common Factor of 12 and 20 is 4. For more conceptual knowledge, students can make use of the article Highest Common Factor drafted by BYJU’S subject experts. Let us learn the simple steps of how to find the Highest Common Factor of 12 and 20 using prime factorisation, long division method and listing common factors in a detailed manner in this article.
What is the HCF of 12 and 20?
The Highest Common Factor of 12 and 20 is 4. In this article, we will learn how to find the Highest Common Factor of 12 and 20 using three methods. They are prime factorisation, long division method and listing common factors.
How to Find HCF of 12 and 20?
There are three methods to find the HCF of 12 and 20:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 12 and 20 by Prime Factorisation Method
In prime factorisation, to find the HCF, we express the given numbers as the product of prime factors. Therefore, 12 and 20 can be expressed as;
12 = 2 × 2 × 3
20 = 2 × 2 × 5
Common prime factors of 12 and 20 are 2 and 2.
Therefore,
HCF (12, 20) = 2 × 2 = 4
HCF of 12 and 20 by Long Division Method
In the long division method, we use the following steps to determine the HCF of 12 and 20
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 zero, 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 equal to zero. The last divisor will be the HCF of the given two numbers.
The HCF of 12 and 20 by the long division method is shown below;
Therefore, HCF (12, 20) = 4
HCF of 12 and 20 by Listing the Factors
Here, by listing the common factors, we derive the HCF of 12 and 20. The common factors of 12 and 20 are as follows:
Factors of 12:1, 2, 3, 4, 6, 12
Factors of 20: 1, 2, 4, 5, 10, 20
Hence, HCF (12, 20) = 4
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Video Lesson on Properties of HCF and LCM
Solved Examples
1. What is the greatest number that divides both 12 and 20 exactly?
Solution: 4 is the greatest number that divides both 12 and 20 exactly.
2. What is the LCM if the product of two numbers is 240 and their GCF is 4?
Solution: Given,
GCF = 4
Product of two numbers = 240
LCM × GCF = Product of two numbers
LCM = Product of two numbers / GCF
LCM = 240/4
LCM = 60
Hence the LCM is 60.
Frequently Asked Questions on HCF of 12 and 20
What is the HCF of 12 and 20?
How to find the HCF of 12 and 20 by prime factorisation?
Here, we express the given numbers as the product of prime factors. Thus the numbers 12 and 20 can be expressed as,
12 = 2 × 2 × 3
20 = 2 × 2 × 5
HCF (12, 20) = 2 × 2 = 4
Name the methods used to find the HCF of 12 and 20.
The following methods are used to find the HCF of 12 and 20
Prime Factorisation
Long Division method
Listing common factors
Is the HCF of 12 and 20 the same as the HCF of 4 and 12?
Mention the relation between LCM and HCF of 12 and 20.
The below equation can be used to denote the relation between LCM and HCF of 12 and 20
HCF × LCM = 12 × 20
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