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102 LearnersLast updated on September 24, 2025
GCF of 6 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 schedule events. In this topic, we will learn about the GCF of 6 and 33.
What is the GCF of 6 and 33?
The greatest common factor of 6 and 33 is 3. 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 6 and 33?
To find the GCF of 6 and 33, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 6 and 33 by Using Listing of factors
Steps to find the GCF of 6 and 33 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 6 = 1, 2, 3, 6. Factors of 33 = 1, 3, 11, 33.
Step 2: Now, identify the common factors of them Common factors of 6 and 33: 1, 3.
Step 3: Choose the largest factor The largest factor that both numbers have is 3.
The GCF of 6 and 33 is 3.
GCF of 6 and 33 Using Prime Factorization
To find the GCF of 6 and 33 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 6: 6 = 2 x 3
Prime Factors of 33: 33 = 3 x 11
Step 2: Now, identify the common prime factors The common prime factor is 3.
Step 3: Multiply the common prime factors Since there is only one common prime factor, the GCF is 3.
The Greatest Common Factor of 6 and 33 is 3.
GCF of 6 and 33 Using Division Method or Euclidean Algorithm Method
Find the GCF of 6 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 6 33 ÷ 6 = 5 (quotient),
The remainder is calculated as 33 − (6×5) = 3
The remainder is 3, not zero, so continue the process
Step 2: Now divide the previous divisor (6) by the previous remainder (3)
Divide 6 by 3 6 ÷ 3 = 2 (quotient), remainder = 6 − (3×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 6 and 33 is 3.
Common Mistakes and How to Avoid Them in GCF of 6 and 33
Finding the GCF of 6 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 6, students may mention 4, 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 the GCF of two numbers will always be an even number. But it's not true as 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 6 and 33 Examples
Problem 1
A gardener has 6 roses and 33 tulips. She wants to plant them in rows with the largest possible number of flowers in each row. How many flowers will be in each row?
We should find the GCF of 6 and 33. GCF of 6 and 33 is 3.
There are 3 equal rows. 6 ÷ 3 = 2 33 ÷ 3 = 11
There will be 3 rows, and each row will have 2 roses and 11 tulips.
Explanation
As the GCF of 6 and 33 is 3, the gardener can make 3 rows.
Now divide 6 and 33 by 3.
Each row will have 2 roses and 11 tulips.
Problem 2
A coach has 6 soccer balls and 33 basketballs. He wants to arrange them in kits with the same number of balls in each kit, using the largest possible number of balls per kit. How many balls will be in each kit?
The GCF of 6 and 33 is 3.
So each kit will have 3 balls.
Explanation
There are 6 soccer balls and 33 basketballs.
To find the total number of balls in each kit, we should find the GCF of 6 and 33.
There will be 3 balls in each kit.
Problem 3
A chef has 6 kg of flour and 33 kg of sugar. She wants to divide both into portions of equal weight, using the largest possible weight. What should be the weight of each portion?
For calculating the longest equal weight, we have to calculate the GCF of 6 and 33.
The GCF of 6 and 33 is 3.
The weight of each portion is 3 kg.
Explanation
For calculating the longest weight of the portions first we need to calculate the GCF of 6 and 33 which is 3.
The weight of each portion will be 3 kg.
Problem 4
A musician has two lengths of wire, one 6 meters long and the other 33 meters long. He wants to cut them into the longest possible equal pieces, without any wire left over. What should be the length of each piece?
The musician needs the longest piece of wire. GCF of 6 and 33 is 3.
The longest length of each piece is 3 meters.
Explanation
To find the longest length of each piece of the two wire lengths, 6 meters and 33 meters, respectively, we have to find the GCF of 6 and 33, which is 3 meters.
The longest length of each piece is 3 meters.
Problem 5
If the GCF of 6 and ‘b’ is 3, and the LCM is 66. Find ‘b’.
The value of ‘b’ is 33.
Explanation
GCF × LCM = product of the numbers
3 × 66 = 6 × b
198 = 6b
b = 198 ÷ 6 = 33
FAQs on the Greatest Common Factor of 6 and 33
1.What is the LCM of 6 and 33?
2.Is 6 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 33?
5.Are 6 and 33 prime numbers?
Important Glossaries for GCF of 6 and 33
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 6 are 1, 2, 3, and 6.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 3 are 3, 6, 9, 12, 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 6, the remainder is 3 and the quotient is 5.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 6 and 33 is 66.
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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.
