The HCF of 60 and 84 is 12. The largest factor present in between two or more numbers is denoted as the Highest Common Factor (HCF). Prime factorisation, long division method and listing common factors are the most frequently used methods to find the Highest Common Factor of given numbers. Solving the problems with the help of the article HCF of Two Numbers on a daily basis enables students to obtain proficiency in the HCF concept. Learn the simple techniques to find the Highest Common Factor of 60 and 84 in this article.
What is the HCF of 60 and 84?
The Highest Common Factor (HCF) of 60 and 84 is 12. Therefore, the largest number that divides 60 and 84 exactly is 12. The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, and the factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. Clearly, among these factors, 12 is the highest number present in both 60 and 84.
How to Find HCF of 60 and 84?
The methods used to find the HCF of 60 and 84 are as follows:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 60 and 84 by Prime Factorisation Method
In the prime factorisation method, the numbers can be written as the product of prime factors. Thus, the numbers 60 and 84 can be written as:
60 = 2 × 2 × 3 × 5
84 = 2 × 2 × 3 × 7
The Common prime factors of 60 and 84 are 2, 2 and 3.
Therefore,
HCF of (60, 84) = 2 × 2 × 3 = 12
HCF of 60 and 84 by Long Division Method
In the long division method, we use the following steps to find the HCF of 60 and 84:
Step 1: Divide the largest number by the smallest among the given two numbers.
Step 2: Check the remainder; if it is not zero, then make it a new divisor and mention the previous divisor as the new dividend and continue the division process.
Step 3: Continue this process until we get the remainder equal to zero. The last divisor is considered the HCF of the given two numbers.
The HCF of 60 and 84 by using the long division method is shown below:
HCF (60, 84) = 12
HCF of 60 and 84 by Listing Common Factors
In this method, we list all the factors of given numbers to determine their Highest Common Factor. The following are the factors of 60 and 84:
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Thus, HCF (60, 84) = 12
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Solved Examples
1. What is the HCF of 60 and 84 if their LCM is 420?
Solution:
Given
LCM = 420
We know that
LCM × HCF = 60 × 84
420 × HCF = 60 × 84
HCF = 12
Therefore, the HCF of 60 and 84 is 12.
2. What is the LCM if the product of two numbers is 5040 and their HCF is 12?
Solution: Given,
HCF = 12
Product of numbers = 5040
We know that
LCM × HCF = Product of numbers
LCM × 12 = 5040
LCM = 420
Therefore, the LCM is 420.
Frequently Asked Questions on HCF of 60 and 84
Write the HCF of 60 and 84.
List the methods to find the HCF of 60 and 84.
The below methods are used to find the HCF of 60 and 84:
Prime Factorisation
Long Division Method
Listing Common Factors
Is the HCF of 60 and 84 the same as the HCF of 12 and 60?
What is the LCM if the HCF of 60 and 84 is 12?
We know that
HCF × LCM = 60 × 84
Given
HCF = 12
12 × LCM = 60 × 84
LCM = 420
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