HCF of 40 and 80 is 40. The Highest Common Factor (HCF) of 40 and 80 is defined as the greatest common factor of 40 and 80. It is also called as Greatest Common Divisor (GCD). The article HCF of Two Numbers is the best guide prepared by BYJU’S expert teachers with the aim to enhance the knowledge of the Highest Common Factor among students. Practising the problems with the help of this article also boosts time management and problem-solving skills which are crucial from an exam point of view. Let us grasp the simple technique of how to find the Highest Common Factor of 40 and 80 in detail here.
What is HCF of 40 and 80?
The Highest Common Factor(HCF) or the Greatest Common Divisor (GCD) of 40 and 80 is 40. The common factors of 40 and 80 are 1, 2, 4, 5, 8, 10, 20 and 40 respectively.
How to Find HCF of 40 and 80?
There are three methods to find the HCF of 40 and 80:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 40 and 80 by Prime Factorisation Method
In the prime factorisation method, we need to express the given numbers as the product of prime factors and get the product of the smallest power of each common prime factor. Hence, 40 and 80 can be expressed as;
40 = 2 × 2 × 2 × 5
80 = 2 × 2 × 2 × 2 × 5
Common prime factor of 40 and 80 is 2, 2, 2 and 5
Therefore,
HCF (40, 80) = 2 × 2 × 2 × 5 = 40
HCF of 40 and 80 by Long Division Method
Follow the steps given below to find the Highest Common Factor of 40 and 80 in the division method.
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 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 the HCF of the given two numbers.
The HCF of 40 and 80 by the long division method is as follows;
HCF (40, 80) = 40
HCF of 40 and 80 by Listing the Factors
In this method, to find the HCF, we need to list the factors of given numbers and then choose the largest of all the common factors. The factors of 40 and 80 are given below:
Factors of 40:1, 2, 4, 5, 8, 10, 20, 40
Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
Hence, HCF (40, 80) = 40
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Video Lesson on Properties of HCF and LCM
Solved Examples
1. What is the highest number that divides both 40 and 80 exactly?
Solution: The largest number that divides 40 and 80 exactly is their Highest Common Factor (HCF). To obtain the HCF, we list the factors of 40 and 80
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
Here, 40 is the Highest Common Factor of 40 and 80. Hence, the highest number that divides both 40 and 80 exactly is 40.
2. For two numbers, HCF = 40 and LCM = 80. If one number is 40, what is the other number?
Solution:
Given
HCF = 40
LCM = 80
Let the other number be n
We know that
LCM × HCF = 40 × n
80 × 40 = 40 × n
n = (80 × 40) / 40
n = 80
Therefore the other number is 80.
Frequently Asked Questions on HCF of 40 and 80
What is the HCF of 40 and 80?
Is the HCF of 40 and 80 the same as the HCF of 40 and 120?
What are the methods used to find the HCF of 40 and 80?
The methods used to find the HCF of 40 and 80 are as follows:
Prime Factorisation
Long Division method
Listing common factors
Calculate the HCF of 40 and 80 using prime factorisation.
In the prime factorisation, we express the given numbers as the product of prime factors to obtain the HCF
40 = 2 × 2 × 2 × 5
80 = 2 × 2 × 2 × 2 × 5
Common prime factor of 40 and 80 is 2, 2, 2 and 5
Therefore, HCF (40, 80) = 2 × 2 × 2 × 5 = 40
What is the LCM if the HCF of 40 and 80 is 40?
Given
HCF = 40
HCF × LCM = 40 × 80
40 × LCM = 3200
LCM = 80
Therefore, the LCM is 80
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