The HCF of 108 and 144 is 36. HCF is the greatest integer that can divide 108 and 144 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 108 and 144, the common factors are 1, 2, 3, 4, 6, 9, 12, 18 and 36. Since 36 is the highest among the given factors, HCF would be 36 for 108 and 144. HCF is also termed GCF, which is the Greatest Common Factor. Learn more on GCF.
What is the HCF of 108 and 144?
The Highest Common Factor, also known as the Greatest Common Factor of 108 and 144, is 36.
How to Find HCF of 108 and 144?
There are three methods to find the HCF of 108 and 144:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 108 and 144 by Prime Factorisation Method
In prime factorisation, the numbers can be expressed as the product of prime numbers. Here, 108 and 144 can be expressed as:
108 = 2 × 2 × 3 × 3 × 3
144 = 2 × 2 × 2 × 2 × 3 × 3
The common prime factors of 108 and 144 are 2 × 2 × 3 × 3. Therefore, HCF will be:
HCF (108, 144) = 2 × 2 × 3 × 3 = 36
HCF of 108 and 144 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 108 and 144, the HCF by long division method is:
Therefore, HCF (108, 144) = 36
HCF of 108 and 144 by Listing Common Factors
By listing common factors of given numbers, we can identify the Highest/Greatest/Biggest Common Factor, which is the HCF. Below is the list of factors for 108 and 144:
Factors of 108:
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108
Factors of 144:
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Therefore, HCF (108, 144) = 36
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Video Lesson on Properties of HCF and LCM
Solved Examples
1. Find the HCF of 12, 24 and 36 using the listing common factors.
Solution: Factors of 12 are 1, 2, 3, 4, 6 and 12
Factors of 24 are 1, 2, 3, 4, 6, 8 and 12
Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
The common factors are 1, 2, 3, 4, 6 and 12. Therefore, HCF is 12.
2. What is the second highest factor of 108 and 144?
Solution: 18 is the second highest factor of 108 and 144.
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