The HCF of 25 and 40 is 5. The Highest Common Factor (HCF) is the largest possible number that divides the given numbers exactly without leaving a remainder. HCF of Two Numbers is the best study guide to erase the doubts of students occurring on HCF. Students can refer to this article on a daily basis to obtain in-depth knowledge of the HCF concept. Let us have a look at how to find the Highest Common Factor of 25 and 40 along with solved examples and FAQs in a detailed manner here.
What is the HCF of 25 and 40?
The Highest Common Factor (HCF) or the Greatest Common Divisor (GCD) of 25 and 40 is 5. The given numbers 25 and 40 have only one common prime factor, i.e. 5.
How to Find HCF of 25 and 40?
There are three methods to find the HCF of 25 and 40:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 25 and 40 by Prime Factorisation Method
In the prime factorisation method, we write the given numbers as the product of prime factors. Therefore, 25 and 40 can be written as;
25 = 5 × 5
40 = 2 × 2 × 2 × 5
Common prime factor of 25 and 40 is 5
Hence,
HCF (25, 40) = 5
HCF of 25 and 40 by Long Division Method
We use the following steps to find the Highest Common Factor of 25 and 40 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 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 the HCF of the given two numbers.
The HCF of 25 and 40 by the long division method is as follows:
HCF (25, 40) = 5
HCF of 25 and 40 by Listing the Factors
Here, we list out the common factors of 25 and 40 to find their HCF. The factors of 25 and 40 are mentioned below:
Factors of 25:1, 5, 25
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
Therefore, HCF (25, 40) = 5
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Solved Example
Question: The product of two numbers is 1000. Calculate the LCM if their HCF is 5.
Solution: Given
HCF = 5
Product of numbers = 1000
We know that,
HCF × LCM = Product of numbers
LCM = Product of numbers / HCF
LCM = 1000/5
LCM = 200
Hence the LCM is 200.
Frequently Asked Questions on HCF of 25 and 40
What is the HCF of 25 and 40?
Is the HCF of 25 and 40 the same as the HCF of 5 and 10?
What are the common prime factors of 25 and 40?
Determine the HCF of 25 and 40 using prime factorisation.
To find the HCF of 25 and 40 using prime factorisation, we express the numbers as the product of prime factors
25 = 5 × 5
40 = 2 × 2 × 2 × 5
Common prime factor of 25 and 40 is 5
Therefore, the HCF is 5
Name the methods to determine the HCF of 25 and 40.
The methods used to find the HCF of 25 and 40 are as follows:
Prime Factorisation
Long Division method
Listing common factors
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