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105 LearnersLast updated on September 20, 2025
GCF of 36 and 67
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 schedule events. In this topic, we will learn about the GCF of 36 and 67.
What is the GCF of 36 and 67?
The greatest common factor of 36 and 67 is 1. 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 36 and 67?
To find the GCF of 36 and 67, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / Euclidean Algorithm
GCF of 36 and 67 by Using Listing of Factors
Steps to find the GCF of 36 and 67 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36.
Factors of 67 = 1, 67.
Step 2: Now, identify the common factors of them Common factor of 36 and 67: 1.
Step 3: Choose the largest factor The largest factor that both numbers have is 1.
The GCF of 36 and 67 is 1.
GCF of 36 and 67 Using Prime Factorization
To find the GCF of 36 and 67 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 36: 36 = 2 x 2 x 3 x 3 = 2² x 3²
Prime Factors of 67: 67 is a prime number, so its only prime factors are 1 and 67.
Step 2: Now, identify the common prime factors There are no common prime factors other than 1.
Step 3: Multiply the common prime factors
The GCF of 36 and 67 is 1.
GCF of 36 and 67 Using Division Method or Euclidean Algorithm Method
Find the GCF of 36 and 67 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 67 by 36 67 ÷ 36 = 1 (quotient),
The remainder is calculated as 67 − (36×1) = 31
The remainder is 31, not zero, so continue the process
Step 2: Now divide the previous divisor (36) by the previous remainder (31)
Divide 36 by 31 36 ÷ 31 = 1 (quotient), remainder = 36 − (31×1) = 5
Step 3: Now divide the previous divisor (31) by the previous remainder (5) 31 ÷ 5 = 6 (quotient), remainder = 31 − (5×6) = 1
Step 4: Now divide the previous divisor (5) by the previous remainder (1) 5 ÷ 1 = 5 (quotient), remainder = 5 − (1×5) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 36 and 67 is 1.
Common Mistakes and How to Avoid Them in GCF of 36 and 67
Finding GCF of 36 and 67 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 36, 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 wrong common factor, especially when it is 1. To avoid this confusion, students should list all the common factors and verify that 1 is indeed the only common factor.
Mistake 3
Forgetting to include 1 as a factor
Sometimes students may forget that 1 is a common factor of any two numbers. While it is always included, forgetting it can indicate an incomplete understanding of factors. Students should remember to 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 more than 1
Students may assume that the GCF of two numbers is always more than 1. But when two numbers are co-prime, their GCF is 1. To avoid this, students should focus on the actual common factors.
Greatest Common Factor of 36 and 67 Examples
Problem 1
A chef has 36 tomatoes and 67 cucumbers. She wants to create salad bowls with an equal number of tomatoes and cucumbers in each bowl, using the largest possible number of each. How many of each will be in each bowl?
We should find GCF of 36 and 67 GCF of 36 and 67 is 1.
There will be 1 tomato and 1 cucumber in each bowl.
Explanation
As the GCF of 36 and 67 is 1, the chef can only make bowls with 1 tomato and 1 cucumber.
Problem 2
A museum has 36 paintings and 67 sculptures. They want to arrange them in galleries with the same number of paintings and sculptures in each gallery, using the largest possible number of each. How many of each will be in each gallery?
GCF of 36 and 67 is 1.
So each gallery will have 1 painting and 1 sculpture.
Explanation
To find the number of paintings and sculptures in each gallery, we should find the GCF of 36 and 67, which is 1.
There will be 1 painting and 1 sculpture in each gallery.
Problem 3
A tailor has two rolls of fabric, one 36 meters long and the other 67 meters long. She wants to cut both rolls into pieces of equal length, using the longest possible length. What should be the length of each piece?
For calculating longest equal length, we have to calculate the GCF of 36 and 67
The GCF of 36 and 67 is 1.
The length of each piece will be 1 meter.
Explanation
For calculating the longest length of the fabric pieces, first, we need to calculate the GCF of 36 and 67, which is 1.
The length of each piece of fabric will be 1 meter.
Problem 4
A carpenter has two wooden planks, one 36 cm long and the other 67 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 36 and 67 is 1.
The length of each piece is 1 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 36 cm and 67 cm, respectively, we have to find the GCF of 36 and 67, which is 1 cm.
The length of each piece is 1 cm.
Problem 5
If the GCF of 36 and ‘a’ is 1, and the LCM is 2412. Find ‘a’.
The value of ‘a’ is 67.
Explanation
GCF x LCM = product of the numbers
1 × 2412 = 36 × a
2412 = 36a
a = 2412 ÷ 36 = 67
FAQs on the Greatest Common Factor of 36 and 67
1.What is the LCM of 36 and 67?
2.Is 36 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.Is 67 a prime number?
5.Are 36 and 67 co-prime numbers?
Important Glossaries for GCF of 36 and 67
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
- Prime Number: A prime number is a number greater than 1 that has no positive divisors other than 1 and itself. For example, 67 is a prime number.
- Co-prime: Two numbers are co-prime if their greatest common factor is 1. For example, 36 and 67 are co-prime.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 31 is divided by 5, the remainder is 1.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 36 and 67 is 1, 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.
