102 LearnersLast updated on August 5th, 2025
GCF of 10 and 25
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 10 and 25.
What is the GCF of 10 and 25?
The greatest common factor of 10 and 25 is 5. 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 10 and 25?
To find the GCF of 10 and 25, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method or Euclidean Algorithm
GCF of 10 and 25 by Using Listing of Factors
Steps to find the GCF of 10 and 25 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 10 = 1, 2, 5, 10.
Factors of 25 = 1, 5, 25.
Step 2: Now, identify the common factors of them Common factors of 10 and 25: 1, 5.
Step 3: Choose the largest factor The largest factor that both numbers have is 5.
The GCF of 10 and 25 is 5.
GCF of 10 and 25 Using Prime Factorization
To find the GCF of 10 and 25 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 10: 10 = 2 × 5
Prime Factors of 25: 25 = 5 × 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 10 and 25 is 5.
GCF of 10 and 25 Using Division Method or Euclidean Algorithm Method
Find the GCF of 10 and 25 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number.
Here, divide 25 by 10 25 ÷ 10 = 2 (quotient).
The remainder is calculated as 25 − (10×2) = 5
The remainder is 5, not zero, so continue the process
Step 2: Now divide the previous divisor (10) by the previous remainder (5).
Divide 10 by 5 10 ÷ 5 = 2 (quotient), remainder = 10 − (5×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 10 and 25 is 5.
Common Mistakes and How to Avoid Them in GCF of 10 and 25
Finding GCF of 10 and 25 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 10, students may mention 4, 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 between 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 10 and 25 Examples
Problem 1
A teacher has 10 apples and 25 oranges. 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 10 and 25 GCF of 10 and 25 is 5.
There are 5 equal groups
10 ÷ 5 = 2
25 ÷ 5 = 5
There will be 5 groups, and each group gets 2 apples and 5 oranges.
Explanation
As the GCF of 10 and 25 is 5, the teacher can make 5 groups.
Now divide 10 and 25 by 5. Each group gets 2 apples and 5 oranges.
Problem 2
A school has 10 red chairs and 25 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?
GCF of 10 and 25 is 5. So each row will have 5 chairs.
Explanation
There are 10 red and 25 blue chairs.
To find the total number of chairs in each row, we should find the GCF of 10 and 25.
There will be 5 chairs in each row.
Problem 3
A tailor has 10 meters of red ribbon and 25 meters of blue ribbon. She wants to cut both ribbons 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 10 and 25 The GCF of 10 and 25 is 5. The ribbon is 5 meters long.
Explanation
For calculating the longest length of the ribbon, first we need to calculate the GCF of 10 and 25, which is 5. The length of each piece of the ribbon will be 5 meters.
Problem 4
A carpenter has two wooden planks, one 10 cm long and the other 25 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 10 and 25 is 5. The longest length of each piece is 5 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 10 cm and 25 cm, respectively, we have to find the GCF of 10 and 25, which is 5 cm. The longest length of each piece is 5 cm.
Problem 5
If the GCF of 10 and ‘a’ is 5, and the LCM is 50, find ‘a’.
The value of ‘a’ is 25.
Explanation
GCF × LCM = product of the numbers
5 × 50 = 10 × a
250 = 10a
a = 250 ÷ 10 = 25
FAQs on the Greatest Common Factor of 10 and 25
1.What is the LCM of 10 and 25?
2.Is 10 divisible by 5?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 25?
5.Are 10 and 25 prime numbers?
6.How can children in Indonesia use numbers in everyday life to understand GCF of 10 and 25?
7.What are some fun ways kids in Indonesia can practice GCF of 10 and 25 with numbers?
8.What role do numbers and GCF of 10 and 25 play in helping children in Indonesia develop problem-solving skills?
9.How can families in Indonesia create number-rich environments to improve GCF of 10 and 25 skills?
Important Glossaries for GCF of 10 and 25
- 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 25 are 5 and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 25 is divided by 10, the remainder is 5 and the quotient is 2.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 10 and 25 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.
