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101 LearnersLast updated on September 10, 2025
GCF of 25 and 40
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share the items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 25 and 40.
What is the GCF of 25 and 40?
The greatest common factor of 25 and 40 is 5. The largest divisor of two or more numbers is called the GCF of the numbers. If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1. The GCF of two numbers cannot be negative because divisors are always positive.
How to find the GCF of 25 and 40?
To find the GCF of 25 and 40, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 25 and 40 by Using Listing of Factors
Steps to find the GCF of 25 and 40 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 25 = 1, 5, 25.
Factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40.
Step 2: Now, identify the common factors of them Common factors of 25 and 40: 1, 5.
Step 3: Choose the largest factor The largest factor that both numbers have is 5. The GCF of 25 and 40 is 5.
GCF of 25 and 40 Using Prime Factorization
To find the GCF of 25 and 40 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 25: 25 = 5 × 5 = 5²
Prime Factors of 40: 40 = 2 × 2 × 2 × 5 = 2³ × 5
Step 2: Now, identify the common prime factors The common prime factor is: 5
Step 3: Multiply the common prime factors 5 = 5. The Greatest Common Factor of 25 and 40 is 5.
GCF of 25 and 40 Using Division Method or Euclidean Algorithm Method
Find the GCF of 25 and 40 using the Division Method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 40 by 25 40 ÷ 25 = 1 (quotient), The remainder is calculated as 40 − (25×1) = 15 The remainder is 15, not zero, so continue the process
Step 2: Now divide the previous divisor (25) by the previous remainder (15) Divide 25 by 15 25 ÷ 15 = 1 (quotient), remainder = 25 − (15×1) = 10
Step 3: Divide the previous divisor (15) by the remainder (10) 15 ÷ 10 = 1 (quotient), remainder = 15 − (10×1) = 5
Step 4: Divide the previous divisor (10) by the remainder (5) 10 ÷ 5 = 2 (quotient), remainder = 10 − (5×2) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 25 and 40 is 5.
Common Mistakes and How to Avoid Them in GCF of 25 and 40
Finding the GCF of 25 and 40 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
Mistake 1
Listing Incorrect Factors
Students may sometimes list incorrect factors. For example, while listing factors of 25, students may mention 10, which is incorrect. To avoid this, students should carefully divide the number and list the factors correctly.
Mistake 2
Choosing the Wrong Common Factor
Students may sometimes select the smallest common factor instead of the largest one. To avoid this confusion, students should list all the common factors and find the greatest one.
Mistake 3
Forgetting to Include 1 as a Factor
Sometimes students may forget 1 as a common factor of the numbers. However, it does not affect the GCF, but it tells about the incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples Instead of Factors
Students confuse factors and multiples. In that confusion, sometimes they may write multiples instead of factors. To avoid this confusion, students should know the definitions of multiples and factors clearly.
Mistake 5
Assuming GCF is Always an Even Number
Students may assume that the GCF of two numbers will always be an even number. But it's not true that a GCF can also be an odd number. To avoid this, students should focus on common factors rather than focusing on even and odd numbers.
Greatest Common Factor of 25 and 40 Examples
Problem 1
A farmer has 25 apple trees and 40 orange trees. He wants to plant them in rows with the same number of trees in each row, using the largest possible number of trees per row. How many trees will be in each row?
We should find the GCF of 25 and 40 GCF of 25 and 40 5. So, each row will have 5 trees.
Explanation
As the GCF of 25 and 40 is 5, the farmer can make rows with 5 trees in each.
Problem 2
A chef has 25 kg of flour and 40 kg of sugar. He wants to pack them into bags with the same weight, using the largest possible weight per bag. What should be the weight of each bag?
GCF of 25 and 40 5. So each bag will weigh 5 kg.
Explanation
To pack the flour and sugar into bags of the same weight, we should find the GCF of 25 and 40. Each bag will weigh 5 kg.
Problem 3
A library has 25 fiction books and 40 non-fiction books. The librarian wants to arrange them in sections with the same number of books in each section, using the largest possible number of books per section. How many books will be in each section?
For calculating the largest number of books per section, we have to calculate the GCF of 25 and 40 The GCF of 25 and 40 5. Each section will have 5 books.
Explanation
For calculating the largest number of books per section, first, we need to calculate the GCF of 25 and 40, which is 5. Each section will have 5 books.
Problem 4
A woodworker has two wooden planks, one 25 cm long and the other 40 cm long. He wants to cut them into the longest possible equal pieces, without any wood left over. What should be the length of each piece?
The woodworker needs the longest piece of wood GCF of 25 and 40 5. The longest length of each piece is 5 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 25 cm and 40 cm, respectively, we have to find the GCF of 25 and 40, which is 5 cm. The longest length of each piece is 5 cm.
Problem 5
If the GCF of 25 and ‘a’ is 5, and the LCM is 200, find ‘a’.
The value of ‘a’ is 40.
Explanation
GCF × LCM = product of the numbers 5 × 200 = 25 × a 1000 = 25a a = 1000 ÷ 25 = 40
FAQs on the Greatest Common Factor of 25 and 40
1.What is the LCM of 25 and 40?
2.Is 25 divisible by 5?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 40?
5.Are 25 and 40 prime numbers?
Important Glossaries for GCF of 25 and 40
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 10 are 1, 2, 5, and 10.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 5 are 5, 10, 15, 20, and so on.
- Prime Factors: These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factors of 20 are 2 and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 13 is divided by 5, the remainder is 3 and the quotient is 2.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 25 and 40 is 200.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
