The Highest Common Factor (HCF) of two numbers is the greatest number that can perfectly divide both numbers. In the case of 8 and 16, the HCF is 8. The methods to find the HCF include prime factorisation, long division, and listing common factors. This article will guide you on how to find the HCF of 8 and 16 using these methods.
HCF of 8 and 16: Methods, Examples and FAQs - Testbook.com
Last Updated on Jun 11, 2024
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Understanding the HCF of 8 and 16
The factors of 8 are 1, 2, 4, and 8, while the factors of 16 are 1, 2, 4, 8, and 16. The greatest number that is common to both sets of factors is 8, which is the HCF of 8 and 16.
Methods to Find the HCF of 8 and 16
There are three common methods to find the HCF of any two numbers:
- Prime Factorisation
- Long Division
- Listing Common Factors
Prime Factorisation Method
In the prime factorisation method, we express each number as a product of prime factors. For 8 and 16, we have:
8 = 2 × 2 × 2
16 = 2 × 2 × 2 × 2
The common prime factors are 2, 2, and 2, so the HCF is 2 × 2 × 2 = 8.
Long Division Method
With the long division method, we divide the larger number by the smaller number, then repeat the process with the remainder until there is no remainder. The last divisor is the HCF. For 8 and 16, the HCF is 8.
Listing the Factors Method
By listing all the factors of each number, we can find the largest number common to both lists. For 8 and 16, the factors are:
Factors of 8: 1, 2, 4, 8
Factors of 16: 1, 2, 4, 8, 16
The HCF of 8 and 16 is 8.
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Frequently Asked Questions
What is the HCF of 8 and 16?
The HCF of 8 and 16 is 8.
Is the HCF of 8 and 16 the same as the HCF of 8 and 12?
No. The HCF of 8 and 16 is 8 and the HCF of 8 and 12 is 4.
Name the methods used to find the HCF of 8 and 16.
The methods used to find the HCF of 8 and 16 are as follows: Prime Factorisation, Long Division method, Listing common factors.
How to find the HCF of 8 and 16 using the long division method?
To find the HCF of 8 and 16 using the long division method, we divide the number 16 by 8. The last divisor when the remainder is equal to zero is considered as the HCF of 8 and 16.
Find the LCM if the HCF of 8 and 16 is 8.
We know that HCF × LCM = 8 × 16. Given HCF = 8, so 8 × LCM = 8 × 16, hence the LCM is 16.
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