The HCF of 12, 15 and 21 is 3. The Highest Common Factor (HCF) is the greatest number that divides the given numbers exactly, without leaving any remainder. The article HCF of Two Numbers is designed with the purpose of clearing the doubts of students immediately when they get stuck while solving the problems. It is vital to follow this article on a regular basis for in-depth knowledge of the HCF concept. Let us learn the techniques to find the Highest Common Factor of 12, 15 and 21 using solved examples and FAQs here.
What is the HCF 12, 15 and 21?
The Highest Common Factor (HCF) or the Greatest Common Divisor (GCD) of 12, 15 and 21 is 3. The only common prime factor of 12, 15 and 21 is 3. Hence, the Highest Common Factor of 12, 15 and 21 is 3.
How to Find HCF of 12, 15 and 21?
There are three methods to find the HCF of 12, 15 and 21:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 12, 15 and 21 by Prime Factorisation Method
In the prime factorisation method, to find the HCF, we express the given numbers as the product of prime factors. Hence, 12, 15 and 21 is written as:
12 = 2 × 2 × 3
15 = 3 × 5
21 = 3 × 7
The common prime factor of 12, 15 and 21 is 3.
Therefore,
HCF (12, 15, 21) = 3
HCF of 12, 15 and 21 by Long Division Method
In the long division method, we use the following steps to find the Highest Common Factor of 12, 15 and 21.
Step 1: Divide the number 15 by 12. Here, the remainder is not equal to zero. So, we divide the divisor 12 by the remainder 3. Continue this process till we get the remainder as zero. Thus, the HCF of 12 and 15 is 3.
Step 2: Now, find the HCF of 3 and 21 by performing the long division method on 21 and 3.
Step 3: We get the remainder as zero, and the divisor is 3. Hence, HCF of 3 and 21 is 3.
The HCF of 12, 15 and 21 by the long division method is as follows:
First, we need to divide the number 15 by 12, as given below.
The HCF of 12 and 15 is 3 and the HCF of 3 and 21 is 3
Therefore, the HCF (12, 15, 21) = 3
HCF of 12, 15 and 21 by Listing Common Factors
In this method, we list out all the factors of given numbers to determine their HCF. The factors of 12, 15 and 21 are as follows:
Factors of 12:1, 2, 3, 4, 6, 12
Factors of 15: 1, 3, 5, 15
Factors of 21: 1, 3, 7, 21
Hence, HCF (12, 15, 21) = 3
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Solved Example
Question: Find the highest number that divides 12, 15 and 21 exactly.
Solution: The highest number that divides 12, 15 and 21 exactly is their Highest Common Factor. To find the HCF, we express the factors of 12, 15 and 21.
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 15: 1, 3, 5, 15
Factors of 21: 1, 3, 7, 21
Here, the Highest Common Factor of 12, 15 and 21 is 3. Hence, the highest number that divides 12, 15 and 21 exactly is 3.
Frequently Asked Questions on HCF of 12, 15 and 21
What is the HCF of 12, 15 and 21?
Is the HCF of 12, 15 and 21 the same as the HCF of 3, 9 and 27?
What are the common prime factors of 12, 15 and 21?
What are the methods used to determine the HCF of 12, 15 and 21?
The methods used to determine the HCF of 12, 15 and 21 are:
Prime Factorisation
Long Division method
Listing common factors
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