The HCF of 180, 252 and 324 is 36. The Highest Common Factor (HCF) can be defined as the largest number, which is the factor of two or more numbers. It is also known as the Greatest Common Factor (GCF). Students can excel in the concept of the Highest Common Factor by referring to the HCF article on a regular basis. In Mathematics, students can use different methods to calculate the Highest Common Factor of given numbers. Let us look at the techniques to calculate the Highest Common Factor of 180, 252 and 324 in this article.
What is the HCF of 180, 252 and 324?
The Highest Common Factor of 180, 252 and 324 is 36. The common factors of 180, 252 and 324 are 1, 2, 3, 4, 6, 9, 12, 18 and 36. Hence, 36 is the highest number that divides 180, 252 and 324 exactly.
How to Find HCF of 180, 252 and 324?
There are three methods to find the HCF of 180, 252 and 324:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 180, 252 and 324 by Prime Factorisation Method
In the prime factorisation method, to find the HCF, we express the numbers as the product of prime factors. Therefore, the given numbers 180, 252 and 324 are written as below:
180 = 2 × 2 × 3 × 3 × 5
252 = 2 × 2 × 3 × 3 × 7
324 = 2 × 2 × 3 × 3 × 3 × 3
The common prime factors of 180, 252 and 324 are 2, 2, 3 and 3.
Therefore,
HCF (180, 252, 324) = 2 × 2 × 3 × 3 = 36
HCF of 180, 252 and 324 by Long Division Method
In the long division method, we use the below steps to find the HCF of 180, 252 and 324.
Step 1: Divide the number 252 by 180. We get the divisor as 36 when the remainder is zero. Hence, the HCF of 180 and 252 is 36.
Step 2: Now, perform the division process on 36 and 324 to find the HCF.
Step 3: Again, we get the divisor as 36 when the remainder is zero. Thus, the HCF of 36 and 324 is 36.
The HCF of 180, 252 and 324 by the long division method is shown below:
First, divide the number 252 by 180.
HCF of 180 and 252 is 36 and the HCF of 36 and 324 is 36.
Hence, HCF (180, 252, 324) = 36
HCF of 180, 252 and 324 by Listing Common Factors
In this method, we need all the factors of 180, 252 and 324 to calculate their HCF. The following are the factors of 180, 252 and 324:
Factors of 180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
Factors of 252: 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252
Factors of 324: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324
Hence, HCF (180, 252, 324) = 36
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Solved Example
Question: What is the highest number that divides 180, 252 and 324 exactly?
Solution: The HCF of 180, 252 and 324 is the highest number that divides 180, 252 and 324 exactly. Let us list the factors of the given numbers to find the HCF.
Factors of 180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
Factors of 252: 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252
Factors of 324: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324
Here, the Highest Common Factor of 180, 252 and 324 is 36. Thus, the highest number that divides 180, 252 and 324 exactly is 36.
Frequently Asked Questions on HCF of 180, 252 and 324
What is the HCF of 180, 252 and 324?
How to find the HCF of 180, 252 and 324 by prime factorisation?
In this method, to obtain the HCF, we express the given numbers as the product of prime factors. Therefore, the numbers 180, 252 and 324 can be expressed as:
180 = 2 × 2 × 3 × 3 × 5
252 = 2 × 2 × 3 × 3 × 7
324 = 2 × 2 × 3 × 3 × 3 × 3
The common prime factors of 180, 252 and 324 are 2, 2, 3 and 3
Therefore, HCF (180, 252, 324) = 2 × 2 × 3 × 3 = 36
What are the methods used to find the HCF of 180, 252 and 324?
The methods used to find the HCF of 180, 252 and 324 are as follows:
Prime Factorisation
Long Division method
Listing common factors
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