The HCF of 324 and 144 is 36. The Highest Common Factor is defined as the largest factor present in between two or more numbers. Teachers recommend students to follow the article Highest Common Factor while solving problems for effective calculation, as it provides a detailed explanation of the HCF concept with solved examples and FAQs. It also helps students to clear their doubts instantly and boost their learning process. Let us learn how to find the Highest Common Factor of 324 and 144 using simple techniques in this article.
What is the HCF of 324 and 144?
The Highest Common Factor of 324 and 144 is 36. There are 9 common factors of 324 and 144. They are 1, 2, 3, 4, 6, 9, 12, 18 and 36. Here, the highest number that divides the numbers 324 and 144 is 36.
How to Find HCF of 324 and 144?
The three methods to find the HCF of 324 and 144:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 324 and 144 by Prime Factorisation Method
We represent the numbers as the product of prime factors to find their HCF in the prime factorisation method. Hence, the given numbers 324 and 144 can be expressed as:
324 = 2 × 2 × 3 × 3 × 3 × 3
144 = 2 × 2 × 2 × 2 × 3 × 3
The common prime factors of 324 and 144 are 2, 2, 3 and 3.
Therefore,
HCF (324, 144) = 2 × 2 × 3 × 3 = 36
HCF of 324 and 144 by Long Division Method
In the long division method, we follow the steps given below to find the HCF of 324 and 144.
Step 1: Divide the largest number by the smallest number from the given two numbers.
Step 2: Now, check the remainder. If it is not zero, then make it a new divisor and write the previous divisor as the new dividend. Then perform the division.
Step 3: Continue this process until we get the remainder equal to zero. The last divisor will be considered as the HCF of the given two numbers.
The HCF of 324 and 144 by long division method is shown below:
HCF (324, 144) = 36
HCF of 324 and 144 by Listing Common Factors
In this method, we list the factors of the given numbers and then pick the largest of all the common factors to calculate their Highest Common Factor. The factors of 324 and 144 are provided below:
Factors of 324: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324
Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Hence, HCF (324, 144) = 36
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Solved Examples
1. What is the highest number that divides both 324 and 144 exactly?
Solution: The largest number that divides both 324 and 144 exactly is their HCF. To find the HCF, let us list the factors of 324 and 144:
Factors of 324: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324
Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Here, 36 is the Highest Common Factor of 324 and 144. Hence, the highest number that divides both 324 and 144 is 36.
2. What is the HCF of 324 and 144 if their LCM is 1296?
Solution: Given
LCM = 1296
We know that
LCM × HCF = 324 × 144
1296 × HCF = 324 × 144
HCF = 36
Hence, the HCF of 324 and 144 is 36.
Frequently Asked Questions on HCF of 324 and 144
What is the HCF of 324 and 144?
How to find the HCF of 324 and 144 by prime factorisation?
In this method, we find the HCF by expressing the given numbers as the product of prime factors. Therefore, the numbers 324 and 144 can be represented as:
324 = 2 × 2 × 3 × 3 × 3 × 3
144 = 2 × 2 × 2 × 2 × 3 × 3
The common prime factors of 324 and 144 are 2, 2, 3 and 3.
Therefore, HCF (324, 144) = 2 × 2 × 3 × 3 = 36
List out the common factors of 324 and 144.
What are the methods used to find the HCF of 324 and 144?
The methods used to find the HCF of 324 and 144 are as follows:
Prime Factorisation
Long Division method
Listing common factors
If the HCF of 324 and 144 is 36, what is their LCM?
We know that
HCF × LCM = 324 × 144
Given
HCF = 36
36 × LCM = 324 × 144
LCM = 1296
Hence, the LCM of 324 and 144 is 1296.
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