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107 LearnersLast updated on September 24, 2025
GCF of 18 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 to schedule events. In this topic, we will learn about the GCF of 18 and 25.
What is the GCF of 18 and 25?
The greatest common factor of 18 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 18 and 25?
To find the GCF of 18 and 25, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 18 and 25 by Using Listing of Factors
Steps to find the GCF of 18 and 25 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 18 = 1, 2, 3, 6, 9, 18. Factors of 25 = 1, 5, 25.
Step 2: Now, identify the common factors of them Common factor of 18 and 25: 1.
Step 3: Choose the largest factor The largest factor that both numbers have is 1. The GCF of 18 and 25 is 1.
GCF of 18 and 25 Using Prime Factorization
To find the GCF of 18 and 25 using the Prime Factorization method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 18: 18 = 2 × 3 × 3 = 2 × 3² Prime Factors of 25: 25 = 5 × 5 = 5²
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 18 and 25 is 1.
GCF of 18 and 25 Using Division Method or Euclidean Algorithm Method
Find the GCF of 18 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 18 25 ÷ 18 = 1 (quotient), The remainder is calculated as 25 − (18×1) = 7 The remainder is 7, not zero, so continue the process
Step 2: Now divide the previous divisor (18) by the previous remainder (7) Divide 18 by 7 18 ÷ 7 = 2 (quotient), remainder = 18 − (7×2) = 4 Continue the process
Step 3: Now divide the previous divisor (7) by the previous remainder (4) Divide 7 by 4 7 ÷ 4 = 1 (quotient), remainder = 7 − (4×1) = 3 Continue the process
Step 4: Now divide the previous divisor (4) by the previous remainder (3) Divide 4 by 3 4 ÷ 3 = 1 (quotient), remainder = 4 − (3×1) = 1 Continue the process
Step 5: Now divide the previous divisor (3) by the previous remainder (1) Divide 3 by 1 3 ÷ 1 = 3 (quotient), remainder = 3 − (1×3) = 0 The remainder is zero, the divisor will become the GCF.
The GCF of 18 and 25 is 1.
Common Mistakes and How to Avoid Them in GCF of 18 and 25
Finding GCF of 18 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 18, 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.
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 18 and 25 Examples
Problem 1
A farmer has 18 apple trees and 25 orange trees. He wants to arrange them in rows with the same number of trees in each row, with the maximum number of trees per row. How many trees will be in each row?
We should find the GCF of 18 and 25. The GCF of 18 and 25 is 1. There will be 1 tree in each row.
Explanation
As the GCF of 18 and 25 is 1, the farmer can arrange the trees such that each row has 1 tree for both apple and orange trees.
Problem 2
A baker has 18 loaves of whole wheat bread and 25 loaves of rye bread. He wants to pack them in bags containing the same number of loaves, with the largest number of loaves per bag. How many loaves will each bag contain?
The GCF of 18 and 25 is 1. So each bag will have 1 loaf.
Explanation
There are 18 loaves of whole wheat bread and 25 loaves of rye bread.
To find the total number of loaves in each bag, we should find the GCF of 18 and 25.
There will be 1 loaf in each bag.
Problem 3
A painter has 18 red paint cans and 25 blue paint cans. He wants to use them in projects with the same number of cans, using the maximum possible number of cans per project. How many cans will each project use?
For calculating the maximum number of cans, we have to calculate the GCF of 18 and 25. The GCF of 18 and 25 is 1. Each project will use 1 can.
Explanation
For calculating the maximum number of cans per project, first, we need to calculate the GCF of 18 and 25, which is 1.
Each project will use 1 can.
Problem 4
A tailor has two pieces of cloth, one 18 meters long and the other 25 meters long. She wants to cut them into the longest possible equal pieces, without any cloth left over. What should be the length of each piece?
The tailor needs the longest piece of cloth. The GCF of 18 and 25 is 1. The longest length of each piece is 1 meter.
Explanation
To find the longest length of each piece of the two cloths, 18 meters and 25 meters, respectively, we have to find the GCF of 18 and 25, which is 1 meter.
The longest length of each piece is 1 meter.
Problem 5
If the GCF of 18 and ‘b’ is 1, and the LCM is 450. Find ‘b’.
The value of ‘b’ is 25.
Explanation
GCF × LCM = product of the numbers
1 × 450 = 18 × b
450 = 18b
b = 450 ÷ 18
= 25
FAQs on the Greatest Common Factor of 18 and 25
1.What is the LCM of 18 and 25?
2.Is 18 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 25?
5.Are 18 and 25 prime numbers?
Important Glossaries for GCF of 18 and 25
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 18 are 1, 2, 3, 6, 9, and 18.
- Prime Factorization: The process of breaking down a number into its basic prime factors. For example, the prime factorization of 18 is 2 × 3².
- Co-prime Numbers: Two numbers that have only 1 as their greatest common factor. For example, 18 and 25 are co-prime.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 25 is divided by 18, the remainder is 7.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 18 and 25 is 450.
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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.
