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104 LearnersLast updated on October 7, 2025
GCF of 18 and 5
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 5.
What is the GCF of 18 and 5?
The greatest common factor of 18 and 5 is 1.
The largest divisor of two or more numbers is called the GCF of the numbers.
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 5?
To find the GCF of 18 and 5, a few methods are described below -
Listing Factors Prime Factorization Long Division Method / by Euclidean Algorithm
GCF of 18 and 5 by Using Listing of Factors
Steps to find the GCF of 18 and 5 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 5 = 1, 5.
Step 2: Now, identify the common factors of them Common factor of 18 and 5: 1.
Step 3: Choose the largest factor The largest factor that both numbers have is 1.
The GCF of 18 and 5 is 1.
GCF of 18 and 5 Using Prime Factorization
To find the GCF of 18 and 5 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 5: 5 = 5.
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 18 and 5 Using Division Method or Euclidean Algorithm Method
Find the GCF of 18 and 5 using the division method or Euclidean Algorithm Method.
Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 18 by 5 18 ÷ 5 = 3 (quotient), The remainder is calculated as 18 − (5×3) = 3 The remainder is 3, not zero, so continue the process.
Step 2: Now divide the previous divisor (5) by the previous remainder (3) Divide 5 by 3 5 ÷ 3 = 1 (quotient), remainder = 5 − (3×1) = 2.
Step 3: Now divide the previous divisor (3) by the previous remainder (2) Divide 3 by 2 3 ÷ 2 = 1 (quotient), remainder = 3 − (2×1) = 1.
Step 4: Now divide the previous divisor (2) by the previous remainder (1) Divide 2 by 1 2 ÷ 1 = 2 (quotient), remainder = 2 − (1×2) = 0, The remainder is zero; the divisor will become the GCF.
The GCF of 18 and 5 is 1.
Common Mistakes and How to Avoid Them in GCF of 18 and 5
Finding the GCF of 18 and 5 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 a non-existent common factor.
To avoid this confusion, students should list all the common factors and ensure they choose the greatest one, which, in this case, is 1.
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 incomplete understanding of 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 Can Only Be Larger Than 1
Students may assume that the GCF of two numbers must be greater than 1.
But it's not true; if two numbers are co-prime, their GCF is 1.
To avoid this, students should focus on common factors.
Greatest Common Factor of 18 and 5 Examples
Problem 1
A gardener has 18 roses and 5 lilies. She wants to group them into equal sets with the largest number of items in each group. How many items will be in each group?
We should find the GCF of 18 and 5. GCF of 18 and 5 is 1.
There will be 1 group, and each group gets 18 roses and 5 lilies.
Explanation
As the GCF of 18 and 5 is 1, the gardener can make only 1 group.
This means all 18 roses and 5 lilies will be in one group.
Problem 2
A chef has 18 apples and 5 oranges. He wants to arrange them in rows with the same number of fruits in each row, using the largest possible number of fruits per row. How many fruits will be in each row?
GCF of 18 and 5 is 1.
So each row will have 1 fruit.
Explanation
There are 18 apples and 5 oranges.
To find the total number of fruits in each row, we should find the GCF of 18 and 5.
There will be 1 fruit in each row.
Problem 3
A jeweler has 18 grams of gold and 5 grams of silver. She wants to split both into pieces of equal weight, using the longest possible length. What should be the weight of each piece?
For calculating the longest equal weight, we have to calculate the GCF of 18 and 5.
The GCF of 18 and 5 is 1.
The weight of each piece is 1 gram.
Explanation
For calculating the longest weight of the pieces, first, we need to calculate the GCF of 18 and 5, which is 1.
The weight of each piece will be 1 gram.
Problem 4
A construction worker has two metal rods, one 18 cm long and the other 5 cm long. He wants to cut them into the longest possible equal pieces, without any metal left over. What should be the length of each piece?
The worker needs the longest piece of metal. GCF of 18 and 5 is 1.
The longest length of each piece is 1 cm.
Explanation
To find the longest length of each piece of the two metal rods, 18 cm and 5 cm, respectively, we have to find the GCF of 18 and 5, which is 1 cm.
The longest length of each piece is 1 cm.
Problem 5
If the GCF of 18 and 'b' is 1, and the LCM is 90, find 'b'.
The value of 'b' is 5.
Explanation
GCF x LCM = product of the numbers 1 × 90 = 18 × b 90 = 18b b = 90 ÷ 18 = 5
FAQs on the Greatest Common Factor of 18 and 5
1.What is the LCM of 18 and 5?
2.Is 18 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 18?
5.Are 18 and 5 prime numbers?
Important Glossaries for GCF of 18 and 5
- 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 Number: A number greater than 1 with no divisors other than 1 and itself. For example, 5 is a prime number.
- 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 5, the remainder is 3.
- Co-prime: Two numbers are co-prime if their greatest common factor is 1. For example, 18 and 5 are co-prime numbers.
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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.
