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101 LearnersLast updated on September 18, 2025
GCF of 9 and 25
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 9 and 25.
What is the GCF of 9 and 25?
The greatest common factor of 9 and 25 is 1. 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 9 and 25?
To find the GCF of 9 and 25, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 9 and 25 by Using Listing of Factors
Steps to find the GCF of 9 and 25 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 9 = 1, 3, 9.
Factors of 25 = 1, 5, 25.
Step 2: Now, identify the common factors of them Common factor of 9 and 25: 1.
Step 3: Choose the largest factor The largest factor that both numbers have is 1. The GCF of 9 and 25 is 1.
GCF of 9 and 25 Using Prime Factorization
To find the GCF of 9 and 25 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 9: 9 = 3 x 3 = 3²
Prime Factors of 25: 25 = 5 x 5 = 5²
Step 2: Now, identify the common prime factors There are no common prime factors.
Step 3: Since there are no common prime factors, the GCF is 1.
GCF of 9 and 25 Using Division Method or Euclidean Algorithm Method
Find the GCF of 9 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 9 25 ÷ 9 = 2 (quotient), The remainder is calculated as 25 − (9×2) = 7
Step 2: Now divide the previous divisor (9) by the previous remainder (7) 9 ÷ 7 = 1 (quotient), remainder = 9 − (7×1) = 2
Step 3: Now divide the previous divisor (7) by the remainder (2) 7 ÷ 2 = 3 (quotient), remainder = 7 − (2×3) = 1
Step 4: Now divide the previous divisor (2) by the remainder (1) 2 ÷ 1 = 2 (quotient), remainder = 2 − (1×2) = 0 The remainder is zero, so the divisor will become the GCF.
The GCF of 9 and 25 is 1.
Common Mistakes and How to Avoid Them in GCF of 9 and 25
Finding GCF of 9 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 9, students may mention 2, 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 indicates an incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples Instead of Factors
Students confuse factors with 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 any two numbers is always greater than 1. But this is not true, especially if the numbers are co-prime. The GCF can be 1. To avoid this misconception, students should focus on finding common factors.
Greatest Common Factor of 9 and 25 Examples
Problem 1
A gardener has 9 pots and 25 seeds. She wants to distribute the seeds equally among the pots, using the maximum number of seeds in each pot. How many seeds will be in each pot?
We should find the GCF of 9 and 25.
The GCF of 9 and 25 is 1.
There will be 1 seed in each pot.
Explanation
As the GCF of 9 and 25 is 1, the gardener can distribute 1 seed in each pot.
Problem 2
A school has 9 red flags and 25 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?
The GCF of 9 and 25 is 1.
So each row will have 1 flag.
Explanation
There are 9 red flags and 25 blue flags.
To find the total number of flags in each row, we should find the GCF of 9 and 25.
There will be 1 flag in each row.
Problem 3
A tailor has 9 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 9 and 25.
The GCF of 9 and 25 is 1.
The length of each piece will be 1 meter.
Explanation
To calculate the longest length of the ribbon pieces, first, we need to calculate the GCF of 9 and 25, which is 1.
The length of each piece of the ribbon will be 1 meter.
Problem 4
A carpenter has two wooden planks, one 9 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.
The GCF of 9 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, 9 cm and 25 cm, respectively, we have to find the GCF of 9 and 25, which is 1 cm.
The longest length of each piece is 1 cm.
Problem 5
If the GCF of 9 and ‘b’ is 1, and the LCM is 225. Find ‘b’.
The value of ‘b’ is 25.
Explanation
GCF x LCM = product of the numbers
1 × 225 = 9 × b
225 = 9b
b = 225 ÷ 9 = 25
FAQs on the Greatest Common Factor of 9 and 25
1.What is the LCM of 9 and 25?
2.Is 9 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 25?
5.Are 9 and 25 prime numbers?
6.How can families in United States create number-rich environments to improve GCF of 9 and 25 skills?
7.What are some fun ways kids in United States can practice GCF of 9 and 25 with numbers?
8.What role do numbers and GCF of 9 and 25 play in helping children in United States develop problem-solving skills?
9.How can children in United States use numbers in everyday life to understand GCF of 9 and 25?
Important Glossaries for GCF of 9 and 25
Factors: Factors are numbers that divide the target number completely. For example, the factors of 9 are 1, 3, and 9.
Co-prime: Two numbers are co-prime if their GCF is 1. For example, 9 and 25 are co-prime.
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 9 are 3 and 3.
Remainder: The value left after division when the number cannot be divided evenly. For example, when 25 is divided by 9, the remainder is 7.
LCM: The smallest common multiple of two or more numbers is termed the LCM. For example, the LCM of 9 and 25 is 225.
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.
