103 LearnersLast updated on August 5th, 2025
GCF of 33 and 77
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, group or arrange items, and schedule events. In this topic, we will learn about the GCF of 33 and 77.
What is the GCF of 33 and 77?
The greatest common factor of 33 and 77 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 33 and 77?
To find the GCF of 33 and 77, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 33 and 77 by Using Listing of factors
Steps to find the GCF of 33 and 77 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 33 = 1, 3, 11, 33.
Factors of 77 = 1, 7, 11, 77.
Step 2: Now, identify the common factors of them Common factors of 33 and 77: 1, 11.
Step 3: Choose the largest factor
The largest factor that both numbers have is 11.
The GCF of 33 and 77 is 11.
GCF of 33 and 77 Using Prime Factorization
To find the GCF of 33 and 77 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime Factors of each number
Prime Factors of 33: 33 = 3 x 11
Prime Factors of 77: 77 = 7 x 11
Step 2: Now, identify the common prime factors
The common prime factor is: 11
Step 3: Multiply the common prime factors 11 = 11.
The Greatest Common Factor of 33 and 77 is 11.
GCF of 33 and 77 Using Division Method or Euclidean Algorithm Method
Find the GCF of 33 and 77 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 77 by 33 77 ÷ 33 = 2 (quotient),
The remainder is calculated as 77 − (33×2) = 11
The remainder is 11, not zero, so continue the process
Step 2: Now divide the previous divisor (33) by the previous remainder (11)
Divide 33 by 11 33 ÷ 11 = 3 (quotient), remainder = 33 − (11×3) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 33 and 77 is 11.
Common Mistakes and How to Avoid Them in GCF of 33 and 77
Finding GCF of 33 and 77 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 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; 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 77 Examples
Problem 1
A farmer has 33 apple trees and 77 orange trees. He wants to arrange them in rows with the same number of trees in each row, using the largest possible number of trees per row. How many trees will be in each row?
We should find the GCF of 33 and 77
GCF of 33 and 77 11
There are 11 equal groups 33 ÷ 11 = 3 77 ÷ 11 = 7
There will be 11 rows, and each row gets 3 apple trees and 7 orange trees.
Explanation
As the GCF of 33 and 77 is 11, the farmer can make 11 rows. Now divide 33 and 77 by 11. Each row gets 3 apple trees and 7 orange trees.
Problem 2
A school has 33 desks and 77 chairs. They want to arrange them in groups with the same number of items in each group, using the largest possible number of items per group. How many items will be in each group?
GCF of 33 and 77 11
So each group will have 11 items.
Explanation
There are 33 desks and 77 chairs. To find the total number of items in each group, we should find the GCF of 33 and 77. There will be 11 items in each group.
Problem 3
A tailor has 33 meters of silk and 77 meters of cotton 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 77
The GCF of 33 and 77 11
The fabric is 11 meters long.
Explanation
For calculating the longest length of the fabric, first we need to calculate the GCF of 33 and 77, which is 11. The length of each piece of the fabric will be 11 meters.
Problem 4
A carpenter has two wooden beams, one 33 cm long and the other 77 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 77 11
The longest length of each piece is 11 cm.
Explanation
To find the longest length of each piece of the two wooden beams, 33 cm and 77 cm, respectively, we have to find the GCF of 33 and 77, which is 11 cm. The longest length of each piece is 11 cm.
Problem 5
If the GCF of 33 and ‘b’ is 11, and the LCM is 231. Find ‘b’.
The value of ‘b’ is 77.
Explanation
GCF x LCM = product of the numbers 11 × 231 = 33 × b
2541 = 33b
b = 2541 ÷ 33 = 77
FAQs on the Greatest Common Factor of 33 and 77
1.What is the LCM of 33 and 77?
2.Is 33 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 77?
5.Are 33 and 77 prime numbers?
6.How can children in India use numbers in everyday life to understand GCF of 33 and 77?
7.What are some fun ways kids in India can practice GCF of 33 and 77 with numbers?
8.What role do numbers and GCF of 33 and 77 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve GCF of 33 and 77 skills?
Important Glossaries for GCF of 33 and 77
- 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 the products we get by multiplying a given number by another. For example, the multiples of 7 are 7, 14, 21, 28, 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 77 are 7 and 11.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 33 is divided by 8, the remainder is 1 and the quotient is 4.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 33 and 77 is 231.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 33 and 77 will be 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.
