The HCF of 12, 16 and 18 is 2. The largest factor that divides 12, 16 and 18 completely without leaving any remainder is defined as the Highest Common Factor (HCF) of 12, 16 and 18. Students who grasp the HCF concept in-depth, solve the tricky problems on HCF with speed and accuracy. The article HCF of Two Numbers is drafted by expert faculty in simple and understandable language with the aim to offer the best study guide for students. Learn the easy method of how to calculate the Highest Common Factor of 12, 16 and 18 with a complete explanation in this article.
What is the HCF 12, 16 and 18?
The Highest Common Factor (HCF) or the Greatest Common Divisor (GCD) of 12, 16 and 18 is 2. The number 2 is the only common prime factor of 12, 16 and 18. Hence, the Highest Common Factor of 12, 16 and 18 is 2.
How to Find HCF of 12, 16 and 18?
There are three methods to find the HCF of 12, 16 and 18:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 12, 16 and 18 by Prime Factorisation Method
In the prime factorisation method, we denote the given numbers as the product of prime factors to obtain their HCF. Hence, 12, 16 and 18 is expressed as:
12 = 2 × 2 × 3
16 = 2 × 2 × 2 × 2
18 = 2 × 3 × 3
The common prime factor of 12, 16 and 18 is 2.
Therefore,
HCF (12, 16, 18) = 2
HCF of 12, 16 and 18 by Long Division Method
In the long division method, we use the following steps to find the Highest Common Factor of 12, 16 and 18.
Step 1: Divide the number 18 by 16. We get the divisor as 2 when the remainder is zero. Therefore the HCF of 16 and 18 is 2.
Step 2: Now, find the HCF of 2 and 12 by performing the long division method on 12 and 2.
Step 3: Here, we get the divisor as 2 when the remainder becomes zero. Hence, the HCF of 2 and 12 is 2.
The HCF of 12, 16 and 18 by the long division method is as follows:
First, we need to divide the number 18 by 16, as given below
The HCF of 16 and 18 is 2 and the HCF of 2 and 12 is 2
Therefore, the HCF (12, 16, 18) = 2
HCF of 12, 16 and 18 by Listing Common Factors
In this method, we need to list all the factors of 12, 16 and 18 to obtain their HCF. The factors of 12, 16 and 18 are as follows:
Factors of 12:1, 2, 3, 4, 6, 12
Factors of 16: 1, 2, 4, 8, 16
Factors of 18: 1, 2, 3, 6, 9, 18
Hence, HCF (12, 16, 18) = 2
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Solved Example
Question: Find the highest number that divides 12, 16 and 18 exactly.
Solution: The highest number that divides 12, 16 and 18 exactly is their Highest Common Factor. To determine the HCF, we express the factors of 12, 16 and 18.
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 16: 1, 2, 4, 8, 16
Factors of 18: 1, 2, 3, 6, 9, 18
Here, the Highest Common Factor of 12, 16 and 18 is 2. Therefore the highest number that divides 12, 16 and 18 exactly is 2.
Frequently Asked Questions on HCF of 12, 16 and 18
What is the HCF of 12, 16 and 18?
Is the HCF of 12, 16 and 18 the same as the HCF of 2, 6 and 8?
Which of the following is the HCF of 12, 16 and 18? 4, 6, 2, 10
What are the methods used to determine the HCF of 12, 16 and 18?
The methods used to determine the HCF of 12, 16 and 18 are mentioned below:
Prime Factorisation
Long Division method
Listing common factors
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