The HCF of 72, 108 and 180 is 36. HCF of 72, 108 and 180 is the greatest integer that can divide these evenly. HCF stands for Highest Common Factor. For a given set of numbers, there would be common factors, and as the name suggests, the highest among the common factors is known as the HCF. In the given set of numbers 72, 108 and 180, the common factors are 1, 2, 3, 4, 6, 9, 12, 18 and 36. Since 36 is the highest among the common factors, HCF would be 36 for 72, 108 and 180. HCF is also termed GCF, which is the Greatest Common Factor. Learn more on GCF.
What is the HCF of 72, 108 and 180?
The Highest Common Factor, also known as the Greatest Common Factor, of 72, 108 and 180 is 36.
How to Find HCF of 72, 108 and 180?
There are three methods to find the HCF of 72, 108 and 180:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 72, 108 and 180 by Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 72, 108 and 180 can be expressed as:
72 = 2 × 2 × 2 × 3 × 3
108 = 2 × 2 × 3 × 3 × 3
180 = 2 × 2 × 3 × 3 × 5
Common prime factors are 2, 2, 3 and 3. Therefore, HCF will be,
HCF (72, 108, 180) = 2 × 2 × 3 × 3 = 36.
HCF of 72, 108 and 180 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 and the third number are taken 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 three numbers.
HCF of 72, 108 and 180 by long division method is:
Stage 1: Choosing 72 and 108 for 1st Long Division, HCF of 72 and 108 is 36.
Stage 2: Choosing HCF and next number for Long Division. HCF from the previous Long Division = 36, and the left-out number is 180. The HCF is 36.
The division of both stages is shown in the image below.
Hence, HCF of (72, 108, 180) = 36
HCF of 72, 108 and 180 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 72, 108 and 180:
Factors of 72: 1, 2, 3, 4, 36, 8, 9, 12, 18, 24, 36 and 72
Factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108.
Factors of 180:1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90 and 180.
Therefore, HCF (72, 108, 180) = 36
Related Articles
Video Lesson on Properties of HCF and LCM
Solved Examples
1. Find the greatest number that divides 72, 144 and 36 evenly.
The greatest number that divides 72, 144 and 36 is nothing but the GCF, which is 36.
2. What is the second HCF for 72, 108 and 180?
The second HCF for 72, 108 and 180 is 18.
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