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109 LearnersLast updated on August 12, 2025
GCF of 11 and 33
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 11 and 33.
What is the GCF of 11 and 33?
The greatest common factor of 11 and 33 is 11. 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 11 and 33?
To find the GCF of 11 and 33, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 11 and 33 by Using Listing of factors
Steps to find the GCF of 11 and 33 using the listing of factors:
Step 1: Firstly, list the factors of each number: Factors of 11 = 1, 11. Factors of 33 = 1, 3, 11, 33.
Step 2: Now, identify the common factors of them: Common factors of 11 and 33: 1, 11.
Step 3: Choose the largest factor: The largest factor that both numbers have is 11. The GCF of 11 and 33 is 11.
GCF of 11 and 33 Using Prime Factorization
To find the GCF of 11 and 33 using Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number:
Prime Factors of 11: 11 = 11
Prime Factors of 33: 33 = 3 x 11
Step 2: Now, identify the common prime factors: The common prime factor is: 11
Step 3: Multiply the common prime factors: The greatest common factor of 11 and 33 is 11.
GCF of 11 and 33 Using Division Method or Euclidean Algorithm Method
Find the GCF of 11 and 33 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number: Here, divide 33 by 11 33 ÷ 11 = 3 (quotient), The remainder is calculated as 33 − (11×3) = 0
The remainder is zero, so the divisor will become the GCF. The GCF of 11 and 33 is 11.
Common Mistakes and How to Avoid Them in GCF of 11 and 33
Finding GCF of 11 and 33 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 11, students may mention 2, 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 indicates an 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 11 and 33 Examples
Problem 1
A teacher has 11 notebooks and 33 markers. 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 11 and 33. The GCF of 11 and 33 is 11. There are 11 equal groups. 11 ÷ 11 = 1 33 ÷ 11 = 3 There will be 11 groups, and each group gets 1 notebook and 3 markers.
Explanation
As the GCF of 11 and 33 is 11, the teacher can make 11 groups. Now divide 11 and 33 by 11. Each group gets 1 notebook and 3 markers.
Problem 2
A school has 11 red flags and 33 blue flags. They want to arrange them in rows with the same number of flags in each row, using the largest possible number of flags per row. How many flags will be in each row?
The GCF of 11 and 33 is 11. So, each row will have 11 flags.
Explanation
There are 11 red and 33 blue flags. To find the total number of flags in each row, we should find the GCF of 11 and 33. There will be 11 flags in each row.
Problem 3
A tailor has 11 meters of red fabric and 33 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 11 and 33. The GCF of 11 and 33 is 11. The fabric is 11 meters long.
Explanation
For calculating the longest length of the fabric, first we need to calculate the GCF of 11 and 33, which is 11. The length of each piece of fabric will be 11 meters.
Problem 4
A carpenter has two wooden planks, one 11 cm long and the other 33 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 11 and 33 is 11. The longest length of each piece is 11 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 11 cm and 33 cm, respectively, we have to find the GCF of 11 and 33, which is 11 cm. The longest length of each piece is 11 cm.
Problem 5
If the GCF of 11 and ‘a’ is 11, and the LCM is 33. Find ‘a’.
The value of ‘a’ is 33.
Explanation
GCF x LCM = product of the numbers
11 × 33 = 11 × a
363 = 11a
a = 363 ÷ 11 = 33
FAQs on the Greatest Common Factor of 11 and 33
1.What is the LCM of 11 and 33?
2.Is 11 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 33?
5.Are 11 and 33 prime numbers?
Important Glossaries for GCF of 11 and 33
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 11 are 1 and 11.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 11 are 11, 22, 33, 44, 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 33 are 3 and 11.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 33 is divided by 11, the remainder is 0, and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 11 and 33 is 33.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 11 and 33 is 11, 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.
