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105 LearnersLast updated on September 24, 2025
GCF of 36 and 216
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 216.
What is the GCF of 36 and 216?
The greatest common factor of 36 and 216 is 36. 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 36 and 216?
To find the GCF of 36 and 216, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 36 and 216 by Using Listing of Factors
Steps to find the GCF of 36 and 216 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 216 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216.
Step 2: Now, identify the common factors of them Common factors of 36 and 216: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Step 3: Choose the largest factor The largest factor that both numbers have is 36. The GCF of 36 and 216 is 36.
GCF of 36 and 216 Using Prime Factorization
To find the GCF of 36 and 216 using 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 216: 216 = 2 x 2 x 2 x 3 x 3 x 3 = 2³ x 3³
Step 2: Now, identify the common prime factors The common prime factors are: 2 x 2 x 3 x 3 = 2² x 3²
Step 3: Multiply the common prime factors 2² x 3² = 4 x 9 = 36. The Greatest Common Factor of 36 and 216 is 36.
GCF of 36 and 216 Using Division Method or Euclidean Algorithm Method
Find the GCF of 36 and 216 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 216 by 36 216 ÷ 36 = 6 (quotient), The remainder is calculated as 216 − (36 x 6) = 0
The remainder is zero, so the divisor becomes the GCF. The GCF of 36 and 216 is 36.
Common Mistakes and How to Avoid Them in GCF of 36 and 216
Finding the GCF of 36 and 216 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 10, 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 indicates an 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 36 and 216 Examples
Problem 1
A florist has 36 roses and 216 lilies. She wants to create bouquets with the largest possible number of flowers in each bouquet. How many flowers will be in each bouquet?
We should find the GCF of 36 and 216 GCF of 36 and 216 2² x 3² = 4 x 9 = 36. There are 36 flowers in each bouquet. 36 ÷ 36 = 1 216 ÷ 36 = 6 There will be 1 bouquet, and each bouquet gets 36 flowers.
Explanation
As the GCF of 36 and 216 is 36, the florist can make 1 bouquet.
Now divide 36 and 216 by 36.
The bouquet gets 36 flowers.
Problem 2
A warehouse has 36 boxes of apples and 216 boxes of oranges. They want to stack them in rows with the same number of boxes in each row, using the largest possible number of boxes per row. How many boxes will be in each row?
GCF of 36 and 216 2² x 3² = 4 x 9 = 36. So each row will have 36 boxes.
Explanation
There are 36 boxes of apples and 216 boxes of oranges.
To find the total number of boxes in each row, we should find the GCF of 36 and 216.
There will be 36 boxes in each row.
Problem 3
A ribbon maker has 36 meters of red ribbon and 216 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 36 and 216. The GCF of 36 and 216 2² x 3² = 4 x 9 = 36. The ribbon is 36 meters long.
Explanation
For calculating the longest length of the ribbon, first, we need to calculate the GCF of 36 and 216, which is 36.
The length of each piece of the ribbon will be 36 meters.
Problem 4
A carpenter has two wooden planks, one 36 cm long and the other 216 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 216 2² x 3² = 4 x 9 = 36. The longest length of each piece is 36 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 36 cm and 216 cm, respectively, we have to find the GCF of 36 and 216, which is 36 cm.
The longest length of each piece is 36 cm.
Problem 5
If the GCF of 36 and ‘a’ is 18, and the LCM is 648. Find ‘a’.
The value of ‘a’ is 108.
Explanation
GCF x LCM = product of the numbers
18 x 648 = 36 x a
11664 = 36a
a = 11664 ÷ 36
= 324
FAQs on the Greatest Common Factor of 36 and 216
1.What is the LCM of 36 and 216?
2.Is 36 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 216?
5.Are 36 and 216 prime numbers?
Important Glossaries for GCF of 36 and 216
- 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.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 6 are 6, 12, 18, 24, 30, 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 36 are 2 and 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 36 is divided by 5, the remainder is 1 and the quotient is 7.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 36 and 216 is 216.
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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.
