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102 LearnersLast updated on October 25, 2025
GCF of 6 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 6 and 25.
What is the GCF of 6 and 25?
The greatest common factor of 6 and 25 is 1.
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 6 and 25?
To find the GCF of 6 and 25, a few methods are described below -
Listing Factors Prime Factorization Long Division Method / by Euclidean Algorithm
GCF of 6 and 25 by Using Listing of Factors
Steps to find the GCF of 6 and 25 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 6 = 1, 2, 3, 6. Factors of 25 = 1, 5, 25.
Step 2: Now, identify the common factors of them Common factors of 6 and 25: 1.
Step 3: Choose the largest factor The largest factor that both numbers have is 1.
The GCF of 6 and 25 is 1.
GCF of 6 and 25 Using Prime Factorization
To find the GCF of 6 and 25 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 6: 6 = 2 x 3 Prime Factors of 25: 25 = 5 x 5.
Step 2: Now, identify the common prime factors There are no common prime factors.
Step 3: Multiply the common prime factors Since there are no common prime factors, the GCF is 1.
The Greatest Common Factor of 6 and 25 is 1.
GCF of 6 and 25 Using Division Method or Euclidean Algorithm Method
Find the GCF of 6 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 6 25 ÷ 6 = 4 (quotient), The remainder is calculated as 25 − (6×4) = 1 The remainder is 1, not zero, so continue the process.
Step 2: Now divide the previous divisor (6) by the previous remainder (1) Divide 6 by 1 6 ÷ 1 = 6 (quotient), remainder = 6 − (1×6) = 0 The remainder is zero, the divisor will become the GCF.
The GCF of 6 and 25 is 1.
Common Mistakes and How to Avoid Them in GCF of 6 and 25
Finding GCF of 6 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 6, 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 greater than 1
Students may assume that the GCF of two numbers will always be greater than 1.
But it's not true as the GCF can also be 1, especially for co-prime numbers.
To avoid this, students should focus on common factors rather than assumptions.
Greatest Common Factor of 6 and 25 Examples
Problem 1
A gardener has 6 tulips and 25 roses. She wants to plant them in equal groups, with the largest number of flowers in each group. How many flowers will be in each group?
We should find the GCF of 6 and 25 GCF of 6 and 25 is 1.
There are 1 equal group. 6 ÷ 1 = 6 25 ÷ 1 = 25.
There will be 1 group, and each group gets 6 tulips and 25 roses.
Explanation
As the GCF of 6 and 25 is 1, the gardener can make 1 group. Now divide 6 and 25 by 1.
Each group gets 6 tulips and 25 roses.
Problem 2
A school has 6 red markers and 25 blue markers. They want to distribute them equally among the students, using the largest possible number of markers per student. How many markers will each student receive?
GCF of 6 and 25 is 1.
So each student will receive 1 marker.
Explanation
There are 6 red and 25 blue markers.
To find the total number of markers each student receives, we should find the GCF of 6 and 25.
Each student will receive 1 marker.
Problem 3
A tailor has 6 meters of red fabric and 25 meters of blue fabric. She wants to cut both fabrics 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 6 and 25.
The GCF of 6 and 25 is 1.
The fabric is 1 meter long.
Explanation
For calculating the longest length of the fabric, first we need to calculate the GCF of 6 and 25 which is 1.
The length of each piece of fabric will be 1 meter.
Problem 4
A carpenter has two wooden planks, one 6 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 6 and 25 is 1.
The longest length of each piece is 1 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 6 cm and 25 cm, respectively. We have to find the GCF of 6 and 25, which is 1 cm.
The longest length of each piece is 1 cm.
Problem 5
If the GCF of 6 and ‘b’ is 1, and the LCM is 150. Find ‘b’.
The value of ‘b’ is 25.
Explanation
GCF x LCM = product of the numbers 1 × 150 = 6 × b 150 = 6b b = 150 ÷ 6 = 25
FAQs on the Greatest Common Factor of 6 and 25
1.What is the LCM of 6 and 25?
2.Is 25 divisible by 5?
3.What will be the GCF of any two co-prime numbers?
4.What is the prime factorization of 6?
5.Are 6 and 25 prime numbers?
Important Glossaries for GCF of 6 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 3 are 3, 6, 9, 12, 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 14 is divided by 4, the remainder is 2 and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 5 and 6 is 30.
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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.
