The HCF of 16 and 64 is 16. The largest number that divides both 16 and 64 exactly is defined as the Highest Common Factor of 16 and 64. The factors of 16 are 1, 2, 4, 8, 16, and the factors of 64 are 1, 2, 4, 8, 16, 32, 64. Clearly, 16 is the largest number present in both 16 and 64. Hence, we can conclude that the Highest Common Factor of 16 and 64 is 16. Students who are having trouble learning the HCF concept are advised to follow the article HCF of Two Numbers to grasp the concept easily in a short period of time. Let us learn the tricks on how to calculate the Highest Common Factor of 16 and 64, using solved examples and FAQs in this article.
What is the HCF of 16 and 64?
The Highest Common Factor (HCF) of 16 and 64 is 16. In this article, we will learn the simple tricks of how to find the Highest Common Factor of 16 and 64 using prime factorisation, long division method and listing common factors.
How to Find HCF of 16 and 64?
Let us look at the methods used to find the HCF of 16 and 64:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 16 and 64 by Prime Factorisation Method
In prime factorisation, the numbers are expressed as the product of prime factors. Hence, the numbers 16 and 64 are written as:
16 = 2 × 2 × 2 × 2
64 = 2 × 2 × 2 × 2 × 2 × 2
Therefore,
HCF of (16, 64) = 2 × 2 × 2 × 2 = 16
HCF of 16 and 64 by Long Division Method
In the long division method, go through the steps given below to find the Highest Common Factor of 16 and 64.
Step 1: Divide the largest number by the smallest among the given two numbers
Step 2: Check the remainder; if it is not zero, then make it a new divisor and mention the previous divisor as the new dividend and continue the division process.
Step 3: Repeat this process until we get the remainder equal to zero. The last divisor is considered the HCF of the given two numbers.
The HCF of 16 and 64 by using the long division method is given below:
HCF (16, 64) = 16
HCF of 16 and 64 by Listing Common Factors
In this method, to find the HCF, we need to list out the factors of given numbers and choose the largest of all the common prime factors.
Factors of 16: 1, 2, 4, 8, 16
Factors of 64: 1, 2, 4, 8, 16, 32, 64
Hence, HCF (16, 64) = 16
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Video Lesson on Properties of HCF and LCM
Solved Example
Question: Calculate the LCM if the product of two numbers is 1024 and their HCF is 16.
Solution: Given
HCF = 16
Product of two numbers = 1024
We know that:
LCM × HCF = Product of two numbers
LCM × 16 = 1024
LCM = 1024/16
LCM = 64
Therefore, the LCM is 64.
Frequently Asked Questions on HCF of 16 and 64
What is the HCF of 16 and 64?
List out the methods used to find the HCF of 16 and 64.
The following three methods are used to find the HCF of 16 and 64:
Prime Factorisation
Long Division method
Listing common factors
Is 54 the LCM of 16 and 64?
Write the relation between LCM and HCF of 16 and 64.
The following equation can be used to express the relation between LCM and HCF of 16 and 64:
HCF × LCM = 16 × 64
Find the HCF of 16 and 64 by using the prime factorisation method.
In the prime factorisation method, we express the given numbers as the product of prime factors to calculate their HCF.
16 = 2 × 2 × 2 × 2
64 = 2 × 2 × 2 × 2 × 2 × 2
The common prime factors of 16 and 64 are 2, 2, 2 and 2.
Therefore, HCF of (16, 64) = 2 × 2 × 2 × 2 = 16
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