The HCF of 27 and 63 is 9. In Maths, the full form of HCF is the Highest Common Factor. The factors of 27 and 63 are 1, 3, 9, 27 and 1, 3, 7, 9, 21, and 63, respectively. The greatest among these factors in both the numbers is 9. Therefore, we can conclude that 9 is the Highest Common Factor of 27 and 63. The article HCF is designed by BYJU’S experts in simple language so that students can grasp the HCF concept more effectively irrespective of their intelligence quotient. Here, we will learn how to find the Highest Common Factor of 27 and 63 using different methods in a precise manner.
What is the HCF of 27 and 63?
The answer to this question is 9. There are three common factors of 27 and 63. They are 1, 3, and 9. Hence, the Highest Common Factor of 27 and 63 is 9.
How to Find HCF of 27 and 63?
There are three methods to find the HCF of 27 and 63:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 27 and 63 by Prime Factorisation Method
Here, we write the numbers as the product of prime factors. To find the Highest Common Factor, multiply all the common prime factors with the lowest degree (power).
27 = 3 × 3 × 3
63 = 3 × 3 × 7
Common prime factors of 27 and 63 are 3 and 3.
Therefore, HCF of (27, 63) = 3 × 3 = 9
HCF of 27 and 63 by Long Division Method
In the division method, we divide the largest number by the smallest among the given numbers until the remainder is zero. The last divisor will be the Highest Common Factor of given numbers.
HCF (27, 63) = 9
HCF of 27 and 63 by Listing the Factors
In this method, we can find the Highest Common Factor by listing all the factors of given numbers. The factors of 27 and 63 are as follows:
Factors of 27: 1, 3, 9, 27
Factors of 63: 1, 3, 7, 9, 21, 63
Therefore, HCF (27, 63) = 9
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Video Lesson on Properties of HCF and LCM
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Solved Example
Question: What is the HCF of 27 and 63 if their LCM is 189?
Solution: We know that,
LCM × HCF = 27 × 63
HCF (27, 63) = (27 × 63)/LCM
HCF (27, 63) = (27 × 63) / 189
HCF (27, 63) = 9
Hence, the HCF of 27 and 63 is 9.
Frequently Asked Questions on HCF of 27 and 63
What is the HCF of 27 and 63?
What are the methods used to find the HCF of 27 and 63?
There are three methods to find the HCF of 27 and 63. They are as follows:
Prime Factorisation
Long Division Method
Listing Common Factors
Find the number that divides 27 and 63 exactly.
Determine the LCM if the HCF of 27 and 63 is 9.
We know that
HCF × LCM = 27 × 63
Given
HCF = 9
9 × LCM = 27 × 63
LCM = 189
Therefore, the LCM is 189.
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