The HCF of 84 and 98 is 14. The largest number that divides the given numbers 84 and 98 evenly is 14. The common factors of 84 and 98 are 1, 2, 7, and 14. Students who are looking for the best guide to clarify their doubts on the HCF concept can rely on the article Highest Common Factor. Practising the HCF-related problems with the help of this article boosts time management and problem-solving skills among students. Learn the simple technique of how to verify the Highest Common Factor of 84 and 98 with a detailed explanation in this article.
What is the HCF of 84 and 98?
The Highest Common Factor of 84 and 98 is 14. There are 4 common factors of 84 and 98. They are 1, 2, 7, and 14. Hence the Highest Common Factor of 84 and 98 is 14.
How to Find HCF of 84 and 98?
There are three methods to find the HCF of 84 and 98:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 84 and 98 by Prime Factorisation Method
To find the HCF by the prime factorisation method, we express the numbers as the product of prime factors. The given numbers 84 and 98 can be represented as;
84 = 2 × 2 × 3 × 7
98 = 2 × 7 × 7
Common prime factors of 84 and 98 are 2 and 7.
Therefore,
HCF (84, 98) = 2 × 7 = 14
HCF of 84 and 98 by Long Division Method
In the long division method, we use the following steps to determine the HCF of 84 and 98
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 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 98 by the long division method is;
Hence, HCF (84, 98) = 14
HCF of 84 and 98 by Listing the Factors
In this method, we can find the HCF of 84 and 98 by listing out their factors. The factors of 84 and 98 are as follows:
Factors of 84:1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Factors of 98: 1, 2, 7, 14, 49, 98
Hence, HCF (84, 98) = 14
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Solved Examples
1. What is the highest number that divides both 84 and 98 exactly?
Solution: The Highest Common Factor of 84 and 98 is 14. Hence 14 is the highest number that divides both 84 and 98 exactly.
2. What is the HCF of 84 and 98 if their LCM is 588?
Solution: Given
LCM = 588
We know that
LCM × HCF = 84 × 98
HCF = (84 × 98)/LCM
HCF = (84 × 98)/588
HCF = 8232 / 588 = 14
Hence the HCF of 84 and 98 is 14.
Frequently Asked Questions on HCF of 84 and 98
What is the HCF of 84 and 98?
How to find the HCF of 84 and 98 by prime factorisation?
In this method, we express the given numbers as the product of prime factors. Therefore the numbers 84 and 98 can be expressed as:
84 = 2 × 2 × 3 × 7
98 = 2 × 7 × 7
HCF (84, 98) = 2 × 7 = 14
Name the methods used to find the HCF of 84 and 98.
The methods used to find the HCF of 84 and 98 are as follows:
Prime Factorisation
Long Division method
Listing common factors
Find the LCM if the HCF of 84 and 98 is 14.
We know that
HCF × LCM = 84 × 98
Given
HCF = 14
14 × LCM = 84 × 98
LCM = 588
Hence the LCM is 588
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