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101 LearnersLast updated on September 24, 2025
GCF of 18 and 26
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 18 and 26.
What is the GCF of 18 and 26?
The greatest common factor of 18 and 26 is 2. 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 26?
To find the GCF of 18 and 26, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 18 and 26 by Using Listing of factors
Steps to find the GCF of 18 and 26 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 26 = 1, 2, 13, 26.
Step 2: Now, identify the common factors of them Common factors of 18 and 26: 1, 2.
Step 3: Choose the largest factor The largest factor that both numbers have is 2. The GCF of 18 and 26 is 2.
GCF of 18 and 26 Using Prime Factorization
To find the GCF of 18 and 26 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 18: 18 = 2 x 3 x 3 = 2 x 3² Prime Factors of 26: 26 = 2 x 13
Step 2: Now, identify the common prime factors The common prime factor is: 2
Step 3: Multiply the common prime factors 2 = 2. The Greatest Common Factor of 18 and 26 is 2.
GCF of 18 and 26 Using Division Method or Euclidean Algorithm Method
Find the GCF of 18 and 26 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 26 by 18 26 ÷ 18 = 1 (quotient), The remainder is calculated as 26 − (18×1) = 8 The remainder is 8, not zero, so continue the process
Step 2: Now divide the previous divisor (18) by the previous remainder (8) Divide 18 by 8 18 ÷ 8 = 2 (quotient), remainder = 18 − (8×2) = 2 The remainder is 2, not zero, so continue the process
Step 3: Now divide the previous divisor (8) by the previous remainder (2) Divide 8 by 2 8 ÷ 2 = 4 (quotient), remainder = 0 The remainder is zero, the divisor will become the GCF. The GCF of 18 and 26 is 2.
Common Mistakes and How to Avoid Them in GCF of 18 and 26
Finding the GCF of 18 and 26 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 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 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 26 Examples
Problem 1
A baker has 18 cupcakes and 26 cookies. She wants to arrange them into trays with the largest equal number of items in each tray. How many items will be in each tray?
We should find the GCF of 18 and 26. GCF of 18 and 26 is 2. There are 2 equal trays. 18 ÷ 2 = 9 26 ÷ 2 = 13 There will be 2 trays, each with 9 cupcakes and 13 cookies.
Explanation
As the GCF of 18 and 26 is 2, the baker can make 2 trays.
Now divide 18 and 26 by 2.
Each tray gets 9 cupcakes and 13 cookies.
Problem 2
A farmer has 18 apple trees and 26 orange trees. She wants to plant them in rows with the same number of trees in each row, using the largest possible number of trees per row. How many trees will be in each row?
GCF of 18 and 26 is 2. So each row will have 2 trees.
Explanation
There are 18 apple trees and 26 orange trees.
To find the total number of trees in each row, we should find the GCF of 18 and 26.
There will be 2 trees in each row.
Problem 3
A cook has 18 meters of red fabric and 26 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 18 and 26. The GCF of 18 and 26 is 2. The fabric is 2 meters long.
Explanation
For calculating the longest length of the fabric, first we need to calculate the GCF of 18 and 26, which is 2.
The length of each piece of the fabric will be 2 meters.
Problem 4
A carpenter has two wooden planks, one 18 cm long and the other 26 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 18 and 26 is 2. The longest length of each piece is 2 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 18 cm and 26 cm, respectively, we have to find the GCF of 18 and 26, which is 2 cm.
The longest length of each piece is 2 cm.
Problem 5
If the GCF of 18 and ‘b’ is 2, and the LCM is 234, find ‘b’.
The value of ‘b’ is 26.
Explanation
GCF x LCM = product of the numbers
2 × 234 = 18 × b
468 = 18b
b = 468 ÷ 18
= 26
FAQs on the Greatest Common Factor of 18 and 26
1.What is the LCM of 18 and 26?
2.Is 18 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 26?
5.Are 18 and 26 prime numbers?
Important Glossaries for GCF of 18 and 26
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 18 are 1, 2, 3, 6, 9, and 18.
- 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, 15, 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 18 are 2 and 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 18 is divided by 8, the remainder is 2 and the quotient is 2.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 18 and 26 is 234.
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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.
