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103 LearnersLast updated on September 24, 2025
GCF of 36 and 3
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 36 and 3.
What is the GCF of 36 and 3?
The greatest common factor of 36 and 3 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.
How to find the GCF of 36 and 3?
To find the GCF of 36 and 3, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / Euclidean Algorithm
GCF of 36 and 3 by Using Listing of Factors
Steps to find the GCF of 36 and 3 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 3 = 1, 3.
Step 2: Now, identify the common factors of them Common factors of 36 and 3: 1, 3.
Step 3: Choose the largest factor The largest factor that both numbers have is 3. The GCF of 36 and 3 is 3.
GCF of 36 and 3 Using Prime Factorization
To find the GCF of 36 and 3 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 36: 36 = 2 × 2 × 3 × 3 = 2² × 3² Prime Factors of 3: 3 = 3¹
Step 2: Now, identify the common prime factors The common prime factor is: 3¹
Step 3: Multiply the common prime factors 3¹ = 3. The Greatest Common Factor of 36 and 3 is 3.
GCF of 36 and 3 Using Division Method or Euclidean Algorithm Method
Find the GCF of 36 and 3 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 3 36 ÷ 3 = 12 (quotient), The remainder is calculated as 36 − (3 × 12) = 0
Since the remainder is zero, the divisor will become the GCF. The GCF of 36 and 3 is 3.
Common Mistakes and How to Avoid Them in GCF of 36 and 3
Finding the GCF of 36 and 3 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 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 the GCF of two numbers will always be an even number. But it's not true that 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 3 Examples
Problem 1
A baker has 36 cookies and 3 trays. She wants to distribute the cookies equally among the trays, using the largest number of cookies per tray. How many cookies will be in each tray?
We should find the GCF of 36 and 3. GCF of 36 and 3 is 3. 36 ÷ 3 = 12 There will be 12 cookies in each tray.
Explanation
As the GCF of 36 and 3 is 3, the baker can distribute the cookies equally among the trays.
Each tray will have 12 cookies.
Problem 2
A school has 36 desks and 3 classrooms. They want to arrange them with the same number of desks in each classroom, using the largest possible number of desks per classroom. How many desks will be in each classroom?
GCF of 36 and 3 is 3. So each classroom will have 12 desks.
Explanation
There are 36 desks and 3 classrooms.
To find the total number of desks in each classroom, we should find the GCF of 36 and 3.
Each classroom will have 12 desks.
Problem 3
A florist has 36 roses and 3 vases. She wants to arrange them in the vases with the same number of roses in each vase, using the largest possible number of roses per vase. How many roses will be in each vase?
For an equal arrangement, we have to calculate the GCF of 36 and 3. The GCF of 36 and 3 is 3. Each vase will have 12 roses.
Explanation
For the equal arrangement of roses in the vases, first, we need to calculate the GCF of 36 and 3, which is 3.
Each vase will have 12 roses.
Problem 4
A tailor has a piece of fabric 36 meters long and wants to cut it into pieces of equal length that are each 3 meters long. How many pieces will she have?
The tailor needs the longest piece of fabric. GCF of 36 and 3 is 3. The fabric will be cut into 12 pieces.
Explanation
To cut the fabric into the longest equal pieces, we need to find the GCF of 36 and 3, which is 3.
Therefore, the fabric will be cut into 12 pieces.
Problem 5
If the GCF of 36 and ‘b’ is 3, and the LCM is 108, find ‘b’.
The value of ‘b’ is 9.
Explanation
GCF × LCM = product of the numbers
3 × 108 = 36 × b
324 = 36b
b = 324 ÷ 36
= 9
FAQs on the Greatest Common Factor of 36 and 3
1.What is the LCM of 36 and 3?
2.Is 36 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 3?
5.Are 36 and 3 prime numbers?
Important Glossaries for GCF of 36 and 3
- 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 Factors: These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factor of 3 is 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 3, the remainder is 1.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 36 and 3 is 36.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 36 and 3 is 3, 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.
