HCF of 12, 24 and 36 is 12. The Highest Common Factor (HCF) is defined as the largest positive integer that divides the given numbers completely. The article HCF of Two Numbers is the best study source to obtain the knowledge of HCF concept with ease. Students who aspire to improve their skills in solving the HCF problems are advised to follow this article on a regular basis. Let us understand the simple tricks of how to find the Highest Common Factor of 12, 24 and 36 with a complete explanation in this article.
What is HCF of 12, 24 and 36?
The Highest Common Factor(HCF) or the Greatest Common Divisor (GCD) of 12, 24 and 36 is 12. There are six common factors of 12, 24 and 36. They are 1, 2, 3, 4, 6 and 12. Therefore, 12 is the Highest Common Factor of 12, 24 and 36.
How to Find HCF of 12, 24 and 36?
There are three methods to find the HCF of 12, 24 and 36:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 12, 24 and 36 by Prime Factorisation Method
In the prime factorisation method, the given numbers are expressed as the product of prime factors to find the Highest Common Factor.
12 = 2 × 2 × 3
24 = 2 × 2 × 2 × 3
36 = 2 × 2 × 3 × 3
Common prime factors of 12, 24 and 36 are 2, 2 and 3.
Therefore,
HCF (12, 24, 36) = 2 × 2 × 3 = 12
HCF of 12, 24 and 36 by Long Division Method
Follow the steps mentioned below to find the Highest Common Factor of 12, 24 and 36 in the division method.
Step 1: Divide the number 24 by 12. We get the divisor as 12 when the remainder is equal to zero. Hence HCF of 12 and 24 is 12
Step 2: Now, find the HCF of 12 and 36 by performing the long division method on 36 and 12
Step 3: Again, we get the divisor as 12 when the remainder becomes zero. Therefore the HCF of 12 and 36 is 12
The HCF of 12, 24 and 36 by the long division method is as follows;
HCF (12, 24) = 12 and the HCF (12, 36) = 12
Therefore HCF of (12, 24, 36) = 12
HCF of 12, 24 and 36 by Listing the Factors
In this method, we need to list out all the factors of given numbers and then pick the largest of all the common factors to find their HCF. The factors of 12, 24 and 36 are as follows:
Factors of 12:1, 2, 3, 4, 6, 12
Factors of 24: 1, 2, 3, 4, 6, 8, 12,24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18,36
Hence, HCF (12, 24, 36) = 12
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Solved Example
Question: What is the highest number that divides 12, 24 and 36 exactly?
Solution: The highest number that divides the numbers 12, 24 and 36 is their Highest Common Factor. To know the HCF, let us list the factors of given numbers. The factors of 12, 24 and 36 are shown below:
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Clearly, 12 is the Highest Common Factor of 12, 24 and 36. Hence the highest number that divides 12, 24 and 36 is 12.
Frequently Asked Questions on HCF of 12, 24 and 36
What is the HCF of 12, 24 and 36?
Is the HCF of 12, 24 and 36 same as the HCF of 12, 48 and 72?
List out the methods used to find the HCF of 12, 24 and 36.
The methods used to find the HCF of 12, 24 and 36 are as follows:
Prime Factorisation
Long Division method
Listing common factors
Find the HCF of 12, 24 and 36 using prime factorisation.
To find the HCF using prime factorisation, we express the given numbers as the product of prime factors.
12 = 2 × 2 × 3
24 = 2 × 2 × 2 × 3
36 = 2 × 2 × 3 × 3
Common prime factors of 12, 24 and 36 are 2, 2 and 3
Therefore, HCF (12, 24, 36) = 2 × 2 × 3 = 12
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