The HCF of 32 and 40 is 8. The largest number, which is the factor of two or more numbers, is called the Highest Common Factor (HCF). The factors of 32 and 40 are 1, 2, 4, 8, 16, 32 and 1, 2, 4, 5, 8, 10, 20, 40, respectively. Among these factors, 8 is the largest number, which divides both 32 and 40. Hence, the Highest Common Factor of 32 and 40 is 8. To obtain proficiency in finding the HCF of given numbers, students are advised to follow the article HCF on a daily basis. In this article, let us learn the tricks of how to find the Highest Common Factor of 32 and 40 using prime factorisation, the long division method and the listing of common factors.
What is the HCF of 32 and 40?
The Highest Common Factor of 32 and 40 is 8. There are four common factors of 32 and 40. They are 1, 2, 4 and 8. Therefore, the Highest Common Factor of 32 and 40 is 8.
How to Find HCF of 32 and 40?
There are three methods to find the HCF of 32 and 40:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 32 and 40 by Prime Factorisation Method
In the prime factorisation method, we express the numbers as the product of prime factors. Therefore, the given numbers 32 and 40 can be represented as:
32 = 2 × 2 × 2 × 2 × 2
40 = 2 × 2 × 2 × 5
The common prime factors of 32 and 40 are 2, 2 and 2.
Therefore,
HCF (32, 40) = 2 × 2 × 2 = 8
HCF of 32 and 40 by Long Division Method
In the long division method, we use the following steps to determine the HCF of 32 and 40.
Step 1: We divide the largest number by the smallest number from the given two numbers.
Step 2: Now, check the remainder. If it is not zero, 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 considered as the HCF of the given two numbers.
The HCF of 32 and 40 by the long division method is:
HCF (32, 40) = 8
HCF of 32 and 40 by Listing Common Factors
In this method, we list out the factors of 32 and 40 to determine their HCF. Let us have a look at the factors of 32 and 40 given below.
Factors of 32: 1, 2, 4, 8, 16, 32
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
Hence, HCF (32, 40) = 8
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Solved Examples
1. What is the highest number that divides both 32 and 40 exactly?
Solution: The largest number that divides both 32 and 40 exactly is their Highest Common Factor (HCF). To find the HCF, let us list the factors of 32 and 40.
Factors of 32: 1, 2, 4, 8, 16, 32
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
Here, the HCF of 32 and 40 is 8. Hence, 8 is the highest number that divides both 32 and 40 exactly.
2. What is the LCM if the product of two numbers is 1280 and their HCF is 8?
Solution: Given,
HCF = 8
Product of numbers = 1280
We know that
LCM × HCF = Product of numbers
LCM = Product of numbers/HCF
LCM = 1280/8
LCM = 160
Hence, the LCM is 160.
Frequently Asked Questions on HCF of 32 and 40
What is the HCF of 32 and 40?
How to find the HCF of 32 and 40 by prime factorisation?
In this method, we express the given numbers as the product of prime factors. Therefore, the numbers 32 and 40 can be expressed as:
32 = 2 × 2 × 2 × 2 × 2
40 = 2 × 2 × 2 × 5
HCF (32, 40) = 2 × 2 × 2 = 8
Name the methods to find the HCF of 32 and 40.
The methods used to find the HCF of 32 and 40 are as follows:
Prime Factorisation
Long Division method
Listing common factors
Is the HCF of 32 and 40 and the HCF of 8 and 16 the same?
Find the LCM if the HCF of 32 and 40 is 8.
We know that
HCF × LCM = 32 × 40
Given
HCF = 8
8 × LCM = 32 × 40
LCM = 160
Therefore, the LCM is 160
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