Last updated on August 5th, 2025
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.
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.
To find the GCF of 33 and 77, a few methods are described below -
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
If the GCF of 33 and ‘b’ is 11, and the LCM is 231. Find ‘b’.
The value of ‘b’ is 77.
GCF x LCM = product of the numbers 11 × 231 = 33 × b
2541 = 33b
b = 2541 ÷ 33 = 77
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.
: She loves to read number jokes and games.