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106 LearnersLast updated on October 7, 2025
GCF of 33 and 99
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 33 and 99.
What is the GCF of 33 and 99?
The greatest common factor of 33 and 99 is 33.
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 33 and 99?
To find the GCF of 33 and 99, a few methods are described below -
Listing Factors Prime Factorization Long Division Method / by Euclidean Algorithm
GCF of 33 and 99 by Using Listing of factors
Steps to find the GCF of 33 and 99 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 33 = 1, 3, 11, 33. Factors of 99 = 1, 3, 9, 11, 33, 99.
Step 2: Now, identify the common factors of them Common factors of 33 and 99: 1, 3, 11, 33.
Step 3: Choose the largest factor The largest factor that both numbers have is 33.
The GCF of 33 and 99 is 33.
GCF of 33 and 99 Using Prime Factorization
To find the GCF of 33 and 99 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 33: 33 = 3 × 11 Prime Factors of 99: 99 = 3 × 3 × 11.
Step 2: Now, identify the common prime factors, The common prime factors are: 3 × 11.
Step 3: Multiply the common prime factors 3 × 11 = 33.
The Greatest Common Factor of 33 and 99 is 33.
GCF of 33 and 99 Using Division Method or Euclidean Algorithm Method
Find the GCF of 33 and 99 using the division method or Euclidean Algorithm Method.
Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 99 by 33 99 ÷ 33 = 3 (quotient), The remainder is calculated as 99 − (33×3) = 0, The remainder is zero, the divisor will become the GCF.
The GCF of 33 and 99 is 33.
Common Mistakes and How to Avoid Them in GCF of 33 and 99
Finding GCF of 33 and 99 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 33, students may mention 5, 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 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; 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 33 and 99 Examples
Problem 1
A gardener has 33 tulips and 99 roses. She wants to group them into equal sets, with the largest number of flowers in each group. How many flowers will be in each group?
We should find the GCF of 33 and 99 GCF of 33 and 99 3 × 11 = 33.
There are 33 equal groups 33 ÷ 33 = 1 99 ÷ 33 = 3.
There will be 33 groups, and each group gets 1 tulip and 3 roses.
Explanation
As the GCF of 33 and 99 is 33, the gardener can make 33 groups.
Now divide 33 and 99 by 33. Each group gets 1 tulip and 3 roses.
Problem 2
A school has 33 desks and 99 chairs. They want to arrange them in rows with the same number of furniture in each row using the largest possible number of items per row. How many items will be in each row?
GCF of 33 and 99 3 × 11 = 33.
So each row will have 33 items.
Explanation
There are 33 desks and 99 chairs.
To find the total number of items in each row, we should find the GCF of 33 and 99.
There will be 33 items in each row.
Problem 3
A tailor has 33 meters of red fabric and 99 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 33 and 99, The GCF of 33 and 99 3 × 11 = 33.
The fabric is 33 meters long.
Explanation
For calculating the longest length of the fabric first we need to calculate the GCF of 33 and 99 which is 33.
The length of each piece of the fabric will be 33 meters.
Problem 4
A carpenter has two wooden planks, one 33 cm long and the other 99 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 33 and 99 3 × 11 = 33.
The longest length of each piece is 33 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 33 cm and 99 cm, respectively.
We have to find the GCF of 33 and 99, which is 33 cm.
The longest length of each piece is 33 cm.
Problem 5
If the GCF of 33 and ‘a’ is 11, and the LCM is 297. Find ‘a’.
The value of ‘a’ is 99.
Explanation
GCF x LCM = product of the numbers 11 × 297 = 33 × a 3267 = 33a a = 3267 ÷ 33 = 99
FAQs on the Greatest Common Factor of 33 and 99
1.What is the LCM of 33 and 99?
2.Is 33 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 99?
5.Are 33 and 99 prime numbers?
Important Glossaries for GCF of 33 and 99
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 33 are 1, 3, 11, and 33.
- Multiple: Multiples are products we get by multiplying a given number by another. For example, the multiples of 3 are 3, 6, 9, 12, 15, 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 99 are 3 and 11.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 3, the remainder is 1, and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 33 and 99 is 99.
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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.
