The HCF of 6, 72 and 120 is 6. The largest positive integer that divides the numbers without leaving a remainder is considered the Highest Common Factor (HCF) of two or more positive integers. Let us learn the Highest Common Factor by referring to the article HCF designed by experts in simple language. Students who aspire to solve problems based on HCF effortlessly are advised to follow the article prepared by experts on a daily basis. In this article, we learn the simple method to find the Highest Common Factor of 6, 72 and 120, using solved examples and FAQs in an efficient manner.
What is the HCF of 6, 72 and 120?
The Highest Common Factor (HCF) of 6, 72 and 120 is 6. The factors of 6 are 1, 2, 3, 6,the factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, and the factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. Among these factors, 6 is the Highest Common Factor of 6, 72 and 120.
How to Find HCF of 6, 72 and 120?
Let us look at the methods used to find the HCF of 6, 72 and 120:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 6, 72 and 120 by Prime Factorisation Method
In the prime factorisation, we write the prime factors of 6, 72 and 120 to determine the Highest Common Factor.
6 = 2 × 3
72 = 2 × 2 × 2 × 3 × 3
120 = 2 × 2 × 2 × 3 × 5
The common prime factors of 6, 72 and 120 are 2 and 3.
Therefore,
HCF (6, 72, 120) = 2 × 3 = 6
HCF of 6, 72 and 120 by Long Division Method
Follow the steps given below to find the Highest Common Factor of 6, 72 and 120 using the long division method.
Step 1: First, divide the number 72 by 6.
Step 2: We get the divisor as 6 when the remainder is equal to zero. Hence, the HCF of 6 and 72 is 6.
Step 3: Now, we perform the long division process on 6 and 120 to find the HCF. We get the divisor as 6 when the remainder is zero. Therefore, the HCF of 6 and 120 is 6.
The HCF of 6, 72 and 120 by the long division method is given below:
First, calculate the HCF of 6 and 72
HCF of 6 and 72 is 6 and HCF of 6 and 120 is 6.
Hence, the HCF (6, 72, 120) = 6
HCF of 6, 72 and 120 by Listing Common Factors
In this method, we list out the factors of given numbers and choose the highest of all the common prime factors.
Factors of 6: 1, 2, 3, 6
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Therefore, HCF (6, 72, 120) = 6
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Solved Example
Question: Determine the highest number that divides 6, 72 and 120 completely.
Solution: The number that divides 6, 72 and 120 completely is their Highest Common Factor (HCF). Let us look at the factors of 6, 72 and 120 given below:
Factors of 6: 1, 2, 3, 6
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Hence, the Highest Common Factor of 6, 72 and 120 is 6.
Frequently Asked Questions on HCF of 6, 72 and 120
Write the HCF of 6, 72 and 120.
What are the methods to find the HCF of 6, 72 and 120?
The methods to find the HCF of 6, 72 and 120 are:
Prime Factorisation
Long Division method
Listing common factors
Is 365 the LCM of 6, 72 and 120?
The HCF of 6, 72 and 120 and the HCF of 6, 18 and 42 are the same. True or False.
Find the HCF of 6, 72 and 120 using prime factorisation.
In the prime factorisation, to find the HCF, we write the given numbers as the product of prime factors
6 = 2 × 3
72 = 2 × 2 × 2 × 3 × 3
120 = 2 × 2 × 2 × 3 × 5
The common prime factors of 6, 72 and 120 are 2 and 3
Therefore, the HCF (6, 72, 120) = 2 × 3 = 6
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