The HCF of 20 and 25 is 5. The Highest Common Factor (HCF) of 20 and 25 is defined as the largest number that divides both 20 and 25 evenly. The article HCF of Two Numbers provides simple tricks to find out the HCF of given numbers easily. This article is the perfect guide for students to erase doubts and improve skills, which are essential to score good marks in exams. 1, 2, 4, 5, 10, 20, and 1, 5, 25 are the factors of 20 and 25, respectively. Here, we will learn how to find the Highest Common Factor of 20 and 25 with solved examples and FAQs with a complete explanation.
What is the HCF of 20 and 25?
The Highest Common Factor (HCF) or the Greatest Common Divisor (GCD) of 20 and 25 is 5. The common factors of 20 and 25 are 1 and 5.
How to Find HCF of 20 and 25?
There are three methods to find the HCF of 20 and 25:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 20 and 25 by Prime Factorisation Method
In the prime factorisation method, we express the given numbers as the product of prime factors. Hence, 20 and 25 can be expressed as:
20 = 2 × 2 × 5
25 = 5 × 5
The common prime factor of 20 and 25 is 5.
Therefore,
HCF (20, 25) = 5
HCF of 20 and 25 by Long Division Method
Go through the steps given below to find the Highest Common Factor of 20 and 25 using 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 20 and 25 by the long division method is as follows:
HCF (20, 25) = 5
HCF of 20 and 25 by Listing Common Factors
In this method, to find the HCF, we list out all the factors of given numbers. The factors of 20 and 25 are given below:
Factors of 20:1, 2, 4, 5, 10, 20
Factors of 25: 1, 5, 25
Hence, HCF (20, 25) = 5
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Video Lesson on Properties of HCF and LCM
Solved Examples
1. What is the highest number that divides both 20 and 25 exactly?
Solution: The highest number that divides 20 and 25 exactly is their Highest Common Factor (HCF). The Highest Common Factor of 20 and 25 is 5. Therefore, 5 is the highest number that divides both 20 and 25 exactly.
2. For two numbers, HCF = 5 and LCM = 100. If one number is 20, what is the other number?
Solution:
Given
HCF = 5
LCM = 100
Let the other number be m
We know that
LCM × HCF = 20 × m
100 × 5 = 20 × m
m = (100 × 5)/20
m = 25
Therefore, the other number is 25.
Frequently Asked Questions on HCF of 20 and 25
What is the HCF of 20 and 25?
Is the HCF of 20 and 25 the same as the HCF of 5 and 20?
What are the methods used to find the HCF of 20 and 25?
The methods used to find the HCF of 20 and 25 are as follows:
Prime Factorisation
Long Division method
Listing common factors
Calculate the HCF of 20 and 25 using prime factorisation.
In the prime factorisation, we write the given numbers as the product of prime factors to find the HCF.
20 = 2 × 2 × 5
25 = 5 × 5
Common prime factor of 20 and 25 is 5
Therefore, HCF of 20 and 25 is 5.
What is the LCM if the HCF of 20 and 25 is 5?
We know that;
HCF × LCM = 20 × 25
Given
HCF = 5
5 × LCM = 20 × 25
LCM = 100
Hence, the LCM is 100.
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