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104 LearnersLast updated on September 24, 2025
GCF of 5 and 11
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 5 and 11.
What is the GCF of 5 and 11?
The greatest common factor of 5 and 11 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 5 and 11?
To find the GCF of 5 and 11, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 5 and 11 by Using Listing of Factors
Steps to find the GCF of 5 and 11 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 5 = 1, 5. Factors of 11 = 1, 11.
Step 2: Now, identify the common factors of them Common factors of 5 and 11: 1.
Step 3: Choose the largest factor The largest factor that both numbers have is 1.
The GCF of 5 and 11 is 1.
GCF of 5 and 11 Using Prime Factorization
To find the GCF of 5 and 11 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 5: 5 = 5 Prime Factors of 11: 11 = 11
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. The Greatest Common Factor of 5 and 11 is 1.
GCF of 5 and 11 Using Division Method or Euclidean Algorithm Method
Find the GCF of 5 and 11 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 11 by 5 11 ÷ 5 = 2 (quotient), The remainder is calculated as 11 − (5×2) = 1 The remainder is 1, not zero, so continue the process
Step 2: Now divide the previous divisor (5) by the previous remainder (1) Divide 5 by 1 5 ÷ 1 = 5 (quotient), remainder = 5 − (1×5) = 0 The remainder is zero, the divisor will become the GCF.
The GCF of 5 and 11 is 1.
Common Mistakes and How to Avoid Them in GCF of 5 and 11
Finding GCF of 5 and 11 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 5, 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.
However, since the only common factor of 5 and 11 is 1, there is no confusion in this case.
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 can 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 greater than 1
Students may assume that the GCF of two numbers will always be greater than 1, but it's not true. When two numbers are co-prime, their GCF is 1.
To avoid this, students should focus on finding common factors rather than making assumptions.
Greatest Common Factor of 5 and 11 Examples
Problem 1
A gardener has 5 rose plants and 11 tulip plants. She wants to plant them in equal rows with the same number of each type of plant. What is the largest number of plants that can be in each row?
We should find the GCF of 5 and 11. The GCF of 5 and 11 is 1. There will be 1 plant in each row.
Explanation
As the GCF of 5 and 11 is 1, the gardener can plant 1 plant in each row.
Each row will have 1 plant of either type.
Problem 2
A baker has 5 cupcakes and 11 cookies. He wants to pack them into boxes with the same number of items in each box, using the largest possible number of items per box. How many items will be in each box?
The GCF of 5 and 11 is 1. So each box will have 1 item.
Explanation
There are 5 cupcakes and 11 cookies.
To find the total number of items in each box, we should find the GCF of 5 and 11.
There will be 1 item in each box.
Problem 3
A tailor has 5 meters of red fabric and 11 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 5 and 11. The GCF of 5 and 11 is 1. The length of each piece is 1 meter.
Explanation
For calculating the longest length of the fabric, first, we need to calculate the GCF of 5 and 11, which is 1.
The length of each piece of fabric will be 1 meter.
Problem 4
A carpenter has two wooden planks, one 5 cm long and the other 11 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 5 and 11 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, 5 cm and 11 cm, respectively, we have to find the GCF of 5 and 11, which is 1 cm.
The longest length of each piece is 1 cm.
Problem 5
If the GCF of 5 and ‘b’ is 1, and the LCM is 55, find ‘b’.
The value of ‘b’ is 11.
Explanation
GCF × LCM = product of the numbers
1 × 55 = 5 × b
55 = 5b
b = 55 ÷ 5
= 11
FAQs on the Greatest Common Factor of 5 and 11
1.What is the LCM of 5 and 11?
2.Is 5 a prime number?
3.What will be the GCF of any two distinct prime numbers?
4.What is the prime factorization of 11?
5.Are 5 and 11 prime numbers?
Important Glossaries for GCF of 5 and 11
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 5 are 1 and 5.
- Prime Numbers: Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves. For example, 11 is a prime number.
- Co-prime Numbers: Two numbers are co-prime if their GCF is 1. For example, 5 and 11 are co-prime.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 11 is divided by 5, the remainder is 1.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 5 and 11 is 55.
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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.
