The HCF of 8 and 16 is 8. The Highest Common Factor (HCF) of two numbers is defined as the largest number that divides the given two numbers evenly. We can find the Highest Common Factor of given numbers by using methods such as prime factorisation, long division method and listing common factors. The Highest Common Factor of 8 and 16 is 8. Refer to HCF to learn more about the Highest Common Factor in detail. Let us grasp the simple tricks on how to verify the Highest Common Factor of 8 and 16 using solved examples and FAQs in this article.
What is the HCF of 8 and 16?
The Highest Common Factor of 8 and 16 is 8. The factors of 8 and 16 are 1, 2, 4, 8 and 1, 2, 4, 8, 16, respectively. Among these factors, the Highest Common Factor of 8 and 16 is 8.
How to Find HCF of 8 and 16?
There are three methods to find the HCF of 8 and 16:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 8 and 16 by Prime Factorisation Method
In the prime factorisation, to find the HCF, we express the given numbers as the product of prime factors. Hence, 8 and 16 can be expressed as:
8 = 2 × 2 × 2
16 = 2 × 2 × 2 × 2
Common prime factors of 8 and 16 are 2, 2 and 2.
Hence,
HCF (8, 16) = 2 × 2 × 2 = 8
HCF of 8 and 16 by Long Division Method
In this method, we use the following steps to find the Highest Common Factor of 8 and 16:
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 0, 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 the HCF of the given two numbers.
The Highest Common Factor of 8 and 16 by the long division method is:
Hence, HCF (8, 16) = 8
HCF of 8 and 16 by Listing the Factors
In this method, we list out all the factors of 8 and 16 to determine their Highest Common Factor. The factors of 8 and 16 are given below:
Factors of 8: 1, 2, 4, 8
Factors of 16: 1, 2, 4, 8, 16
Hence, HCF (8, 16) = 8
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Video Lesson on Properties of HCF and LCM
Solved Example
Question: The product of two numbers is 128. What is the LCM if their HCF is 8?
Solution: Given
HCF = 8
Product of two numbers = 128
We know that
LCM × HCF = Product of two numbers
LCM = Product of two numbers / HCF
LCM = 128 / 8
LCM = 16
Hence, the LCM is 16.
Frequently Asked Questions on HCF of 8 and 16
What is the HCF of 8 and 16?
Is the HCF of 8 and 16 the same as the HCF of 8 and 12?
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?
Find the LCM if the HCF of 8 and 16 is 8.
We know that
HCF × LCM = 8 × 16
Given
HCF = 8
8 × LCM = 8 × 16
LCM = 16
Hence the LCM is 16
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