105 LearnersLast updated on August 5th, 2025
GCF of 25 and 50
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 25 and 50.
What is the GCF of 25 and 50?
The greatest common factor of 25 and 50 is 25. The largest divisor of two or more numbers is called the GCF of the number. 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 50?
To find the GCF of 25 and 50, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 25 and 50 by Using Listing of factors
Steps to find the GCF of 25 and 50 using the listing of factors:
Step 1: Firstly, list the factors of each number.
Factors of 25 = 1, 5, 25.
Factors of 50 = 1, 2, 5, 10, 25, 50.
Step 2: Now, identify the common factors of them.
Common factors of 25 and 50: 1, 5, 25.
Step 3: Choose the largest factor:
The largest factor that both numbers have is 25.
The GCF of 25 and 50 is 25.
GCF of 25 and 50 Using Prime Factorization
To find the GCF of 25 and 50 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number:
Prime Factors of 25: 25 = 5 x 5 = 5²
Prime Factors of 50: 50 = 2 x 5 x 5 = 2 x 5²
Step 2: Now, identify the common prime factors.
The common prime factor is: 5 x 5 = 5²
Step 3: Multiply the common prime factors 5² = 25.
The Greatest Common Factor of 25 and 50 is 25.
GCF of 25 and 50 Using Division Method or Euclidean Algorithm Method
Find the GCF of 25 and 50 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 50 by 25 50 ÷ 25 = 2 (quotient), The remainder is calculated as 50 − (25×2) = 0
The remainder is zero, so the divisor will become the GCF.
The GCF of 25 and 50 is 25.
Common Mistakes and How to Avoid Them in GCF of 25 and 50
Finding the GCF of 25 and 50 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. Although it does not affect the GCF, it indicates an 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; 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 50 Examples
Problem 1
A teacher has 25 notebooks and 50 markers. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?
We should find the GCF of 25 and 50. GCF of 25 and 50 = 25.
There are 25 equal groups.
25 ÷ 25 = 1
50 ÷ 25 = 2
There will be 25 groups, and each group gets 1 notebook and 2 markers.
Explanation
As the GCF of 25 and 50 is 25, the teacher can make 25 groups.
Now divide 25 and 50 by 25.
Each group gets 1 notebook and 2 markers.
Problem 2
A school has 25 red flags and 50 blue flags. They want to arrange them in rows with the same number of flags in each row, using the largest possible number of flags per row. How many flags will be in each row?
GCF of 25 and 50 = 25. So each row will have 25 flags.
Explanation
There are 25 red and 50 blue flags. To find the total number of flags in each row, we should find the GCF of 25 and 50. There will be 25 flags in each row.
Problem 3
A tailor has 25 meters of cloth and 50 meters of thread. She wants to cut both into pieces of equal length, using the longest possible length. What should be the length of each piece?
For calculating the longest equal length, we have to calculate the GCF of 25 and 50.
The GCF of 25 and 50 = 25.
The length of each piece is 25 meters.
Explanation
For calculating the longest length of the cloth and thread, first, we need to calculate the GCF of 25 and 50, which is 25. The length of each piece will be 25 meters.
Problem 4
A carpenter has two wooden planks, one 25 cm long and the other 50 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 carpenter needs the longest piece of wood.
GCF of 25 and 50 = 25.
The longest length of each piece is 25 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 25 cm and 50 cm, respectively, we have to find the GCF of 25 and 50, which is 25 cm.
The longest length of each piece is 25 cm.
Problem 5
If the GCF of 25 and ‘a’ is 25, and the LCM is 100, find ‘a’.
The value of ‘a’ is 50.
Explanation
GCF x LCM = product of the numbers
25 × 100 = 25 × a
2500 = 25a
a = 2500 ÷ 25 = 50
FAQs on the Greatest Common Factor of 25 and 50
1.What is the LCM of 25 and 50?
2.Is 25 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 50?
5.Are 25 and 50 prime numbers?
6.How can children in Canada use numbers in everyday life to understand GCF of 25 and 50?
7.What are some fun ways kids in Canada can practice GCF of 25 and 50 with numbers?
8.What role do numbers and GCF of 25 and 50 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve GCF of 25 and 50 skills?
Important Glossaries for GCF of 25 and 50
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 25 are 1, 5, and 25.
- 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, 25, 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 50 are 2 and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 25 is divided by 6, the remainder is 1, and the quotient is 4.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 25 and 50 is 50.
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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.
