The HCF of 24 and 32 is 8. The numbers 1, 2, 3, 4, 6, 8, 12, 24 and 1, 2, 4, 8, 16, 32 are the factors of 24 and 32, respectively. Among these factors, 8 is the highest number that exactly divides the numbers 24 and 32. Hence, 8 is the Highest Common Factor of 24 and 32. The article Highest Common Factor is curated in simple language to enable students to grasp the HCF concept without any difficulty, irrespective of their intelligence quotient. Here, let us learn how to determine the Highest Common Factor of 24 and 32 in a precise manner.
What is the HCF of 24 and 32?
The Highest Common Factor of 24 and 32 is 8. This article provides a detailed explanation of how to find the HCF of 24 and 32 in an easy and understandable manner.
How to Find HCF of 24 and 32?
There are three methods to find the HCF of 24 and 32:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 24 and 32 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 24 and 32 can be represented as;
24 = 2 × 2 × 2 × 3
32 = 2 × 2 × 2 × 2 × 2
Common prime factors of 24 and 32 are 2, 2 and 2.
Therefore,
HCF (24, 32) = 2 × 2 × 2 = 8
HCF of 24 and 32 by Long Division Method
In the long division method, we use the following steps to determine the HCF of 24 and 32
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: Continue this process until we get the remainder as zero. The last divisor will be considered as the HCF of the given two numbers.
The HCF of 24 and 32 by long division method is;
HCF (24, 32) = 8
HCF of 24 and 32 by Listing the Factors
We can determine the HCF of 24 and 32 by listing out their factors in this method. Let us glance at the factors of 24 and 32 given below:
Factors of 24:1, 2, 3, 4, 6, 8, 12, 24
Factors of 32: 1, 2, 4, 8, 16, 32
Hence, HCF (24, 32) = 8
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Solved Examples
1. What is the highest number that divides both 24 and 32 exactly?
Solution: 8 is the highest number that divides both 24 and 32 exactly.
2. What is the HCF of 24 and 32 if their LCM is 96?
Solution: Given
LCM = 96
We know that
LCM × HCF = 24 × 32
HCF = (24 × 32)/LCM
HCF = (24 × 32)/96
HCF = 8
Hence the HCF of 24 and 32 is 8.
Frequently Asked Questions on HCF of 24 and 32
What is the HCF of 24 and 32?
How to find the HCF of 24 and 32 by prime factorisation?
In this method, we express the given numbers as the product of prime factors. Therefore the numbers 24 and 32 can be expressed as:
24 = 2 × 2 × 2 × 3
32 = 2 × 2 × 2 × 2 × 2
HCF (24, 32) = 2 × 2 × 2 = 8
Name the methods to find the HCF of 24 and 32.
The methods used to find the HCF of 24 and 32 are as follows:
Prime Factorisation
Long Division method
Listing common factors
What is the LCM if the HCF of 24 and 32 is 8?
We know that
HCF × LCM = 24 × 32
Given
HCF = 8
8 × LCM = 24 × 32
LCM = 96
Hence the LCM is 96
Mention the relation between LCM and HCF of 24 and 32.
The equation given below is used to express the relation between LCM and HCF of 24 and 32
HCF × LCM = 24 × 32
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