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105 LearnersLast updated on September 24, 2025
GCF of 4 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 4 and 11.
What is the GCF of 4 and 11?
The greatest common factor of 4 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 4 and 11?
To find the GCF of 4 and 11, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 4 and 11 by Using Listing of factors
Steps to find the GCF of 4 and 11 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 4 = 1, 2, 4.
Factors of 11 = 1, 11.
Step 2: Now, identify the common factors of them Common factors of 4 and 11: 1.
Step 3: Choose the largest factor The largest factor that both numbers have is 1.
The GCF of 4 and 11 is 1.
GCF of 4 and 11 Using Prime Factorization
To find the GCF of 4 and 11 using Prime Factorization Method, follow these steps:
Step 1: Find the prime Factors of each number
Prime Factors of 4: 4 = 2 x 2 = 2²
Prime Factors of 11: 11 = 11¹
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 4 and 11 is 1.
GCF of 4 and 11 Using Division Method or Euclidean Algorithm Method
Find the GCF of 4 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 4 11 ÷ 4 = 2 (quotient),
The remainder is calculated as 11 − (4×2) = 3
The remainder is 3, not zero, so continue the process
Step 2: Now divide the previous divisor (4) by the previous remainder (3)
Divide 4 by 3 4 ÷ 3 = 1 (quotient), remainder = 4 − (3×1) = 1
Step 3: 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 4 and 11 is 1.
Common Mistakes and How to Avoid Them in GCF of 4 and 11
Finding GCF of 4 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 4, students may mention 3 which is incorrect. To avoid this, students should carefully divide the number and list the factors correctly.
Mistake 2
Assuming there are no common factors
Students may sometimes assume that two numbers have no common factors at all. However, 1 is always a common factor. To avoid this confusion, students should list all the common factors, including 1, 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 greater than 1
Students may assume that the GCF of two numbers is always more than 1. But it's not true; the GCF can also be 1 if the numbers are co-prime. To avoid this, students should focus on common factors rather than assumptions.
Greatest Common Factor of 4 and 11 Examples
Problem 1
A teacher has 4 apples and 11 oranges. She wants to make fruit baskets with the largest number of fruits in each basket. How many fruits will be in each basket?
We should find GCF of 4 and 11 GCF of 4 and 11 is 1.
There will be 1 fruit in each basket.
Explanation
As the GCF of 4 and 11 is 1, the teacher can only make 1 fruit in each basket.
Problem 2
A gardener has 4 pots and 11 plants. She wants to arrange the pots with the same number of plants in each, using the largest number of plants per pot. How many plants will be in each pot?
GCF of 4 and 11 is 1.
So each pot will have 1 plant.
Explanation
There are 4 pots and 11 plants.
To find the total number of plants in each pot, we should find the GCF of 4 and 11.
Each pot will have 1 plant.
Problem 3
A tailor has 4 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 4 and 11
The GCF of 4 and 11 is 1.
The fabric is cut into 1-meter pieces.
Explanation
For calculating the longest length of the fabric first we need to calculate the GCF of 4 and 11 which is 1.
The length of each piece of the fabric will be 1 meter.
Problem 4
A carpenter has two wooden planks, one 4 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 GCF of 4 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, 4 cm and 11 cm, respectively.
We have to find the GCF of 4 and 11, which is 1 cm.
The longest length of each piece is 1 cm.
Problem 5
If the GCF of 4 and ‘a’ is 1, and the LCM is 44. Find ‘a’.
The value of ‘a’ is 11.
Explanation
GCF x LCM = product of the numbers
1 × 44 = 4 × a
44 = 4a
a = 44 ÷ 4 = 11
FAQs on the Greatest Common Factor of 4 and 11
1.What is the LCM of 4 and 11?
2.Is 4 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 11?
5.Are 4 and 11 prime numbers?
Important Glossaries for GCF of 4 and 11
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 4 are 1, 2, and 4.
- Prime Numbers: These are numbers greater than 1 with 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, 4 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 4, the remainder is 3.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 4 and 11 is 1, as it is their largest common factor that divides the numbers completely.
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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.
