The HCF of 84 and 120 is 12. The largest number that divides 84 and 120 exactly is defined as the Highest Common Factor of 84 and 120. We can find the HCF of given numbers by using prime factorisation, long division method and listing common factors. The article Highest Common Factor provides detailed information on how to calculate the Highest Common Factor of given numbers using simple steps. Students who aspire to boost their problem-solving skills can use this article as a reference guide while practising the problems. In this article, we will learn how to find the Highest Common Factor of 84 and 120 using simple steps.
What is the HCF of 84 and 120?
The Highest Common Factor of 84 and 120 is 12. There are 6 common factors of 84 and 120, and they are 1, 2, 3, 4, 6 and 12. Hence, the Highest Common Factor of 84 and 120 is 12.
How to Find HCF of 84 and 120?
The following three methods are used to find the HCF of 84 and 120:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 84 and 120 by Prime Factorisation Method
In the prime factorisation method, to find the HCF, we can write the numbers as the product of prime factors. Therefore, the given numbers 84 and 120 can be written as:
84 = 2 × 2 × 3 × 7
120 = 2 × 2 × 2 × 3 × 5
Common prime factors of 84 and 120 are 2, 2 and 3.
Therefore, HCF (84, 120) = 2 × 2 × 3 = 12
HCF of 84 and 120 by Long Division Method
In the long division method, we can follow the steps mentioned below to determine the HCF of 84 and 120:
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: Continue this process until we get the remainder equal to zero. The last divisor will be considered as the HCF of the given two numbers.
The HCF of 84 and 120 by the long division method is:
Hence, HCF (84, 120) = 12
HCF of 84 and 120 by Listing Common Factors
In this method, we can find the HCF of 84 and 120 by listing out all their factors. Let us have a look at the factors of 84 and 120 given below:
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Hence, HCF (84, 120) = 12
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Solved Examples
1. What is the highest number that divides both 84 and 120 exactly?
Solution: The highest number that divides both 84 and 120 exactly is their Highest Common Factor. Let us write the factors of 84 and 120 to find their HCF.
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Clearly, 12 is the Highest Common Factor of 84 and 120. Hence, the highest number that divides both 84 and 120 exactly is 12.
2. What is the HCF of 84 and 120 if their LCM is 840?
Solution: Given
LCM = 840
We know that
LCM × HCF = 84 × 120
HCF = (84 × 120)/LCM
HCF = (84 × 120)/840
HCF = 10080 / 840 = 12
Hence, the HCF of 84 and 120 is 12.
Frequently Asked Questions on HCF of 84 and 120
What is the HCF of 84 and 120?
How to find the HCF of 84 and 120 by prime factorisation?
To find the HCF in this method, we can express the given numbers as the product of prime factors. Therefore, the numbers 84 and 120 can be expressed as:
84 = 2 × 2 × 3 × 7
120 = 2 × 2 × 2 × 3 × 5
Common prime factors of 84 and 120 are 2, 2 and 3
Therefore, HCF (84, 120) = 2 × 2 × 3 = 12
What are the methods used to find the HCF of 84 and 120?
The following methods are used to find the HCF of 84 and 120:
Prime Factorisation
Long Division method
Listing common factors
Find the LCM if the HCF of 84 and 120 is 12.
We know that
HCF × LCM = 84 × 120
Given
HCF = 12
12 × LCM = 84 × 120
LCM = 840
Hence, the LCM is 840
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