The HCF of 144 and 180 is 36. The product of the factors that are common to each of the given numbers is known as Highest Common Factor (HCF). Prime factorisation, long division method and listing common factors are the three methods to verify the Highest Common Factor of 144 and 180. Professional teachers at BYJU’S advise students to follow the article Highest Common Factor to obtain the skills of finding the HCF of given numbers with speed and accuracy. Let us have a look at how to find the Highest Common Factor of 144 and 180 with the help of the solved examples and FAQs in this article.
What is the HCF of 144 and 180?
The Highest Common Factor (HCF) of 144 and 180 is 36. There are 9 common factors of 144 and 180. They are 1, 2, 3, 4, 6, 9, 12, 18, and 36. Here, 36 is the largest number; hence, the Highest Common Factor of 144 and 180 is 36.
How to Find HCF of 144 and 180?
There are three methods to find the HCF of 144 and 180:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 144 and 180 by Prime Factorisation Method
In the prime factorisation method, we express the numbers as the product of prime factors. Hence the given numbers 144 and 180 can be denoted as;
144 = 2 × 2 × 2 × 2 × 3 × 3
180 = 2 × 2 × 3 × 3 × 5
Common prime factors of 144 and 180 are 2, 2, 3 and 3.
Therefore,
HCF of (144, 180) = 2 × 2 × 3 × 3 = 36
HCF of 144 and 180 by Long Division Method
Go through the steps given below to find the Highest Common Factor of 144 and 180 using the long division method:
- Step 1: Divide the greatest number by the smallest among the given two numbers
- Step 2: Check the remainder. If it is not zero, make it a new divisor and mention the previous divisor as a new dividend and continue the division.
- Step 3: Repeat this process until we get the remainder equal to zero. The last divisor is considered as the HCF of the given two numbers.
The HCF of 144 and 180 using the long division method is as follows:
Hence, HCF (144, 180) = 36
HCF of 144 and 180 by Listing the Factors
In this method, we find the highest common factor of 144 and 180 by listing out all the factors of given numbers. The factors of 144 and 180 are as follows:
Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Factors of 180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
Therefore, HCF (144, 180) = 36
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Video Lesson on Properties of HCF and LCM
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Solved Example
Question: What is the HCF of 144 and 180 if their LCM is 720?
Solution: Given
LCM = 720
We know that
LCM × HCF = 144 × 180
HCF = (144 × 180) / LCM
HCF = (144 × 180) / 720
HCF = 36
Therefore, the HCF of 144 and 180 is 36.
Frequently Asked Questions on HCF of 144 and 180
What is the HCF of 144 and 180?
List out the methods used to find the HCF of 144 and 180.
There are three methods to find the HCF of 144 and 180. They are as follows:
Prime Factorisation
Long Division Method
Listing Common Factors
36 is the HCF of 144 and 180. True or False?
Calculate the LCM if the HCF of 144 and 180 is 36.
We know that
HCF × LCM = 144 × 180
36 × LCM = 144 × 180
LCM = 720
Hence the LCM is 720.
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