The HCF of 18 and 60 is 6. HCF is the greatest integer that can divide 18 and 60 evenly. HCF stands for Highest Common Factor. As the name suggests, for a given set of numbers, there would be common factors, and the highest among the common factors is known as the HCF. In the given set of numbers 18 and 60, the common factors are 1, 2, 3 and 6. Since 6 is the highest among the given factors, HCF would be 6 for 18 and 60. HCF is also termed as GCF, which is the Greatest Common Factor. Learn more on HCF.
What is the HCF of 18 and 60?
The Highest Common Factor, also known as the Greatest Common Factor, of 18 and 60 is 6.
How to Find HCF of 18 and 60?
There are three methods to find the HCF of 18 and 60:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 18 and 60 by Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 18 and 60 can be expressed as;
18 = 2 × 3 × 3
60 = 2 × 2 × 3 × 5
Common Prime Factors are 2 and 3. Therefore, HCF will be,
HCF (18, 60) = 2 × 3 = 6.
HCF of 18 and 60 by Long Division Method
In the Long Division Method, from the given set of numbers, the smaller number is used as the Divisor to the larger number. The smaller number is divided by the remainder. This step is repeated till the remainder becomes zero.
Detailed steps are as follows;
- From the given set of numbers, the smallest number becomes the Divisor, and the larger number becomes the Dividend.
- In the next step, the smaller number becomes the Dividend, and the remainder becomes the Divisor.
- The above step is followed until the remainder is zero.
- The last Divisor would be the HCF.
For 18 and 60, the HCF by Long Division method is;
Hence, HCF (18, 60) = 6
HCF of 18 and 60 by Listing the Factors
By listing all the factors of given numbers, we can identify the Highest/Greatest/Biggest common factor, which is the HCF. Below is the list of factors for 18 and 60:
Factors of 18: 1, 2, 3, 6, 9 and 18
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60
Therefore, HCF (18, 60) = 6
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Video Lesson on Properties of HCF and LCM
Solved Examples
1. Find the Greatest number that divides 18 and 60?
The Greatest number that divides 18 and 60 is nothing but the GCF, which is 6.
2. What is the HCF for 6, 18 and 60?
The HCF for 6, 18 and 60 is 6, as 6 is the smallest number among the given set of numbers and also the factor for 18 and 60.
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