The HCF of 72 and 84 is 12. The largest number among all the common factors of 72 and 84 is represented as the Highest Common Factor of 72 and 84. The article HCF of Two Numbers is curated with the intention to provide the best study source for the students to grasp the knowledge of the HCF concept thoroughly. Prime factorisation, long division method and listing common factors are the three methods to find the Highest Common Factor of two or more numbers. Let us learn the simple tricks of how to determine the Highest Common Factor of 72 and 84 in a detailed manner here.
What is the HCF of 72 and 84?
The Highest Common Factor (HCF) or the Greatest Common Divisor (GCD) of 72 and 84 is 12. 1, 2, 3, 4, 6 and 12 are the common factors of 72 and 84.
How to Find HCF of 72 and 84?
To find the HCF of 72 and 84, we use the following three methods:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 72 and 84 by Prime Factorisation Method
In the prime factorisation method, we depict the given numbers as the product of prime factors to find their HCF. Thus, 72 and 84 can be expressed as shown below:
72 = 2 × 2 × 2 × 3 × 3
84 = 2 × 2 × 3 × 7
The common prime factors of 72 and 84 are 2, 2 and 3.
Hence,
HCF (72, 84) = 2 × 2 × 3 = 12
HCF of 72 and 84 by Long Division Method
Go through the steps given below to find the Highest Common Factor of 72 and 84 in the division method.
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: Repeat this process until the remainder becomes zero. The last divisor will be the HCF of the given two numbers.
The HCF of 72 and 84 using the long division method is as follows:
Thus, HCF (72, 84) = 12
HCF of 72 and 84 by Listing Common Factors
In this method, we list out all the factors of given numbers to determine their Highest Common Factor. The following are the factors of 72 and 84:
Factors of 72:1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Therefore, HCF (72, 84) = 12
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Solved Examples
1. What is the highest number that divides both 72 and 84 exactly.
Solution: The Highest Common Factor of 72 and 84 is the highest number that divides both 72 and 84 exactly. To find the HCF, we list out the factors of 72 and 84:
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Clearly, 12 is the Highest Common Factor of 72 and 84. Therefore, the highest number that divides both 72 and 84 exactly is 12.
2. Find the HCF of 72 and 84 if their LCM is 504.
Solution:
We know that
LCM × HCF = 72 × 84
504 × HCF = 72 × 84
HCF = 12
Thus, the Highest Common Factor of 72 and 84 is 12.
Frequently Asked Questions on HCF of 72 and 84
What is the HCF of 72 and 84?
Is the HCF of 72 and 84 and the HCF of 12 and 96 the same?
Name the methods used to find the HCF of 72 and 84.
The following methods are used to find the HCF of 72 and 84:
Prime Factorisation
Long Division method
Listing common factors
How to find the HCF of 72 and 84 by prime factorisation?
In this method, we write the given numbers as the product of prime factors as mentioned below:
72 = 2 × 2 × 2 × 3 × 3
84 = 2 × 2 × 3 × 7
The common prime factors of 72 and 84 are 2, 2 and 3.
Hence, HCF (72, 84) = 2 × 2 × 3 = 12
What is the LCM if the HCF of 72 and 84 is 12?
We know that
HCF × LCM = 72 × 84
Given
HCF = 12
12 × LCM = 72 × 84
LCM = 504
Therefore, the LCM is 504
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