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 the items equally, to group or arrange items, and to schedule events. In this topic, we will learn about the GCF of 33 and 36.
The greatest common factor of 33 and 36 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.
To find the GCF of 33 and 36, a few methods are described below:
Steps to find the GCF of 33 and 36 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 33 = 1, 3, 11, 33.
Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36.
Step 2: Now, identify the common factors of them
Common factors of 33 and 36: 1, 3.
Step 3: Choose the largest factor
The largest factor that both numbers have is 3.
The GCF of 33 and 36 is 3.
To find the GCF of 33 and 36 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 36: 36 = 2 x 2 x 3 x 3 = 2² x 3²
Step 2: Now, identify the common prime factors
The common prime factor is: 3
Step 3: Multiply the common prime factors 3 = 3
The Greatest Common Factor of 33 and 36 is 3.
Find the GCF of 33 and 36 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 36 by 33 36 ÷ 33 = 1 (quotient),
The remainder is calculated as 36 − (33×1) = 3
The remainder is 3, not zero, so continue the process
Step 2: Now divide the previous divisor (33) by the previous remainder (3)
Divide 33 by 3 33 ÷ 3 = 11 (quotient), remainder = 33 − (3×11) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 33 and 36 is 3.
Finding the GCF of 33 and 36 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
A teacher has 33 pencils and 36 erasers. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?
We should find the GCF of 33 and 36 GCF of 33 and 36 is 3.
There are 3 equal groups 33 ÷ 3 = 11 36 ÷ 3 = 12
There will be 3 groups, and each group gets 11 pencils and 12 erasers.
As the GCF of 33 and 36 is 3, the teacher can make 3 groups. Now divide 33 and 36 by 3. Each group gets 11 pencils and 12 erasers.
A school has 33 red chairs and 36 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?
GCF of 33 and 36 is 3.
So each row will have 3 chairs.
There are 33 red and 36 blue chairs. To find the total number of chairs in each row, we should find the GCF of 33 and 36. There will be 3 chairs in each row.
A tailor has 33 meters of red ribbon and 36 meters of blue 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 the longest equal length, we have to calculate the GCF of 33 and 36.
The GCF of 33 and 36 is 3.
The ribbon is 3 meters long.
For calculating the longest length of the ribbon, first, we need to calculate the GCF of 33 and 36, which is 3. The length of each piece of the ribbon will be 3 meters.
A carpenter has two wooden planks, one 33 cm long and the other 36 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 36 is 3.
The longest length of each piece is 3 cm.
To find the longest length of each piece of the two wooden planks, 33 cm and 36 cm, respectively, we have to find the GCF of 33 and 36, which is 3 cm. The longest length of each piece is 3 cm.
If the GCF of 33 and ‘a’ is 3, and the LCM is 396, find ‘a’.
The value of ‘a’ is 36.
GCF x LCM = product of the numbers 3 × 396 = 33 × a
1188 = 33a
a = 1188 ÷ 33 = 36
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.