The HCF of 144, 180 and 192 is 12. HCF of 144, 180 and 192 is the greatest integer that can divide the given numbers 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 144, 180 and 192, the common factors are 1, 2, 3, 4, 6, and 12. Since 12 is the highest among the given factors, HCF will be 12 for 144, 180 and 192. HCF is also termed GCF, which is the Greatest Common Factor. Learn more on GCF.
What is the HCF of 144, 180 and 192?
The Highest Common Factor, also known as the Greatest Common Factor, of 144, 180 and 192 is 12.
How to Find HCF of 144, 180 and 192?
There are three methods to find the HCF of 144, 180 and 192:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 144, 180 and 192 by Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 144, 180 and 192 can be expressed as:
144 = 2 × 2 × 2 × 2 × 3 × 3
180 = 2 × 2 × 3 × 3 × 5
192 = 2 × 2 × 2 × 2 × 2 × 2 × 3
Common Prime Factors are 2, 2 and 3.
Therefore, HCF will be,
HCF (144, 180 and 192) = 2 × 2 × 3 = 12.
HCF of 144, 180 and 192 by Long Division Method
In the Long division method, the following steps are followed.
- Choose two numbers from the given set of numbers (Usually, the first two numbers are selected).
- From the chosen 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.
- The HCF obtained and the third number are taken again for a new long division.
- HCF becomes the Divisor, and the other number becomes the dividend.
- Long division is continued until the remainder becomes zero.
- The last divisor is the HCF of all the three numbers.
HCF of 144, 180 and 192 by long division method is:
Stage 1: Choosing 144 and 180 for 1st Long Division, the HCF of 144 and 180 is 36.
Stage 2: Choosing HCF and next number for Long Division.
i.e. HCF from previous Long Division = 36 and left out number is 192. Therefore, HCF (144, 180 and 192) is 12.
Both the divisions are shown the image below;
HCF of (144, 180 and 192) = 12
HCF of 144, 180 and 192 by Listing Common 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 144, 180 and 192:
Factors of 144:
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.
Factors of 180:
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90 and 180.
Factors of 192:
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, and 192.
Hence, HCF (144, 180 and 192) = 12
Related Articles
Video Lesson on Properties of HCF and LCM
Solved Examples
1. Find the Greatest number that divides 180 and 192 evenly.
The Greatest number that divides 108 and 192 is nothing but the GCF, which is 12.
2. What is the second HCF for 144, 180 and 192?
The second HCF for 144, 180 and 192 is 6.
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