105 LearnersLast updated on August 5th, 2025
GCF of 22 and 33
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 22 and 33.
What is the GCF of 22 and 33?
The greatest common factor of 22 and 33 is 11. 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, which are always positive.
How to find the GCF of 22 and 33?
To find the GCF of 22 and 33, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 22 and 33 by Using Listing of factors
Steps to find the GCF of 22 and 33 using the listing of factors:
Step 1: Firstly, list the factors of each number:
Factors of 22 = 1, 2, 11, 22.
Factors of 33 = 1, 3, 11, 33.
Step 2: Now, identify the common factors of them.
Common factors of 22 and 33: 1, 11.
Step 3: Choose the largest factor.
The largest factor that both numbers have is 11.
The GCF of 22 and 33 is 11.
GCF of 22 and 33 Using Prime Factorization
To find the GCF of 22 and 33 using Prime Factorization Method, follow these steps:
Step 1: Find the prime Factors of each number
Prime Factors of 22: 22 = 2 x 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 22 and 33 is 11.
GCF of 22 and 33 Using Division Method or Euclidean Algorithm Method
Find the GCF of 22 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 22 33 ÷ 22 = 1 (quotient), The remainder is calculated as 33 − (22×1) = 11
The remainder is 11, not zero, so continue the process
Step 2: Now divide the previous divisor (22) by the previous remainder (11)
Divide 22 by 11 22 ÷ 11 = 2 (quotient), remainder = 22 − (11×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 22 and 33 is 11.
Common Mistakes and How to Avoid Them in GCF of 22 and 33
Finding GCF of 22 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 22, 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 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 an even number
Students may assume that GCF of two numbers will always be an even number. But it's not true that 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 22 and 33 Examples
Problem 1
A gardener has 22 red tulips and 33 yellow tulips. She wants to arrange them in bouquets with the largest number of tulips in each bouquet. How many tulips will be in each bouquet?
We should find GCF of 22 and 33 GCF of 22 and 33 11. There are 11 bouquets 22 ÷ 11 = 2 33 ÷ 11 = 3 There will be 11 bouquets, and each bouquet gets 2 red tulips and 3 yellow tulips.
Explanation
As the GCF of 22 and 33 is 11, the gardener can make 11 bouquets. Now divide 22 and 33 by 11. Each bouquet gets 2 red tulips and 3 yellow tulips.
Problem 2
A company has 22 computers and 33 monitors. They want to organize them into workstations with the same number of computers and monitors in each workstation, using the largest possible number of items per workstation. How many items will be in each workstation?
GCF of 22 and 33 11. So each workstation will have 11 items.
Explanation
There are 22 computers and 33 monitors.
To find the total number of items in each workstation, we should find the GCF of 22 and 33.
There will be 11 items in each workstation.
Problem 3
A baker has 22 meters of chocolate ribbon and 33 meters of vanilla ribbon. She wants to cut both ribbons into pieces of equal length, using the longest possible length. What should be the length of each piece?
For calculating longest equal length, we have to calculate the GCF of 22 and 33
The GCF of 22 and 33 11.
The ribbon is 11 meters long.
Explanation
For calculating the longest length of the ribbon first we need to calculate the GCF of 22 and 33 which is 11. The length of each piece of the ribbon will be 11 meters.
Problem 4
A carpenter has two wooden beams, one 22 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
GCF of 22 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 beams, 22 cm and 33 cm, respectively.
We have to find the GCF of 22 and 33, which is 11 cm.
The longest length of each piece is 11 cm.
Problem 5
If the GCF of 22 and ‘b’ is 11, and the LCM is 66. Find ‘b’.
The value of ‘b’ is 33.
Explanation
GCF x LCM = product of the numbers
11 × 66 = 22 × b
726 = 22b
b = 726 ÷ 22 = 33
FAQs on the Greatest Common Factor of 22 and 33
1.What is the LCM of 22 and 33?
2.Is 22 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 33?
5.Are 22 and 33 prime numbers?
6.How can children in United States use numbers in everyday life to understand GCF of 22 and 33?
7.What are some fun ways kids in United States can practice GCF of 22 and 33 with numbers?
8.What role do numbers and GCF of 22 and 33 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve GCF of 22 and 33 skills?
Important Glossaries for GCF of 22 and 33
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 11 are 1 and 11.
- Prime Numbers: These are numbers greater than 1 that have no divisors other than 1 and themselves. For example, 11 is a prime number.
- Prime Factorization: This is the expression of a composite number as the product of its prime factors. For example, the prime factorization of 22 is 2 x 11.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 33 is divided by 22, the remainder is 11 and the quotient is 1.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 22 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.
