100 LearnersLast updated on August 5th, 2025
GCF of 15 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, group or arrange items, and schedule events. In this topic, we will learn about the GCF of 15 and 25.
What is the GCF of 15 and 25?
The greatest common factor of 15 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 15 and 25?
To find the GCF of 15 and 25, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 15 and 25 by Using Listing of factors
Steps to find the GCF of 15 and 25 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 15 = 1, 3, 5, 15.
Factors of 25 = 1, 5, 25.
Step 2: Now, identify the common factors of them Common factors of 15 and 25: 1, 5.
Step 3: Choose the largest factor
The largest factor that both numbers have is 5.
The GCF of 15 and 25 is 5.
GCF of 15 and 25 Using Prime Factorization
To find the GCF of 15 and 25 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 15: 15 = 3 x 5
Prime Factors of 25: 25 = 5 x 5 = 5²
Step 2: Now, identify the common prime factors
The common prime factor is: 5
Step 3: Multiply the common prime factors
The Greatest Common Factor of 15 and 25 is 5.
GCF of 15 and 25 Using Division Method or Euclidean Algorithm Method
Find the GCF of 15 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 15 25 ÷ 15 = 1 (quotient),
The remainder is calculated as 25 − (15×1) = 10
The remainder is 10, not zero, so continue the process
Step 2: Now divide the previous divisor (15) by the previous remainder (10)
Divide 15 by 10 15 ÷ 10 = 1 (quotient), remainder = 15 − (10×1) = 5
The remainder is 5, so continue the process
Step 3: Now divide the previous divisor (10) by the previous remainder (5)
Divide 10 by 5 10 ÷ 5 = 2 (quotient), remainder = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 15 and 25 is 5.
Common Mistakes and How to Avoid Them in GCF of 15 and 25
Finding GCF of 15 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 15, students may mention 6, 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 15 and 25 Examples
Problem 1
A gardener has 15 rose bushes and 25 tulip bulbs. She wants to plant them in equal rows, with the largest number of plants in each row. How many plants will be in each row?
We should find the GCF of 15 and 25 GCF of 15 and 25 is 5.
There are 5 equal groups.
15 ÷ 5 = 3 25 ÷ 5 = 5
There will be 5 rows, and each row gets 3 rose bushes and 5 tulip bulbs.
Explanation
As the GCF of 15 and 25 is 5, the gardener can make 5 rows.
Now divide 15 and 25 by 5.
Each row gets 3 rose bushes and 5 tulip bulbs.
Problem 2
A chef has 15 kilograms of flour and 25 kilograms of sugar. She wants to package them into bags with the same weight, using the largest possible weight per bag. How much will each bag weigh?
GCF of 15 and 25 is 5. So each bag will weigh 5 kilograms.
Explanation
There are 15 kilograms of flour and 25 kilograms of sugar.
To find the total weight in each bag, we should find the GCF of 15 and 25.
There will be 5 kilograms in each bag.
Problem 3
A cyclist has a 15-kilometer route and a 25-kilometer route. He wants to divide both routes into equal segments, using the longest possible segment length. How long should each segment be?
For calculating the longest equal segment length, we have to calculate the GCF of 15 and 25
The GCF of 15 and 25 is 5.
Each segment is 5 kilometers long.
Explanation
For calculating the longest segment length of the route, first, we need to calculate the GCF of 15 and 25, which is 5.
The length of each segment of the route will be 5 kilometers.
Problem 4
A musician has two pieces of wire for instruments, one 15 cm long and the other 25 cm long. He wants to cut them into the longest possible equal pieces, without any wire left over. What should be the length of each piece?
The musician needs the longest piece of wire GCF of 15 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 pieces of wire, 15 cm and 25 cm, respectively, we have to find the GCF of 15 and 25, which is 5 cm.
The longest length of each piece is 5 cm.
Problem 5
If the GCF of 15 and ‘a’ is 5, and the LCM is 75. Find ‘a’.
The value of ‘a’ is 25.
Explanation
GCF x LCM = product of the numbers 5 × 75 = 15 × a
375 = 15a
a = 375 ÷ 15 = 25
FAQs on the Greatest Common Factor of 15 and 25
1.What is the LCM of 15 and 25?
2.Is 15 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 25?
5.Are 15 and 25 prime numbers?
6.How can children in United States use numbers in everyday life to understand GCF of 15 and 25?
7.What are some fun ways kids in United States can practice GCF of 15 and 25 with numbers?
8.What role do numbers and GCF of 15 and 25 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve GCF of 15 and 25 skills?
Important Glossaries for GCF of 15 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 25 are 5 and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 3, the remainder is 1, and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 15 and 25 is 75.
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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.
