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103 LearnersLast updated on September 20, 2025
GCF of 36 and 51
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 51.
What is the GCF of 36 and 51?
The greatest common factor of 36 and 51 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 51?
To find the GCF of 36 and 51, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 36 and 51 by Using Listing of factors
Steps to find the GCF of 36 and 51 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 51 = 1, 3, 17, 51.
Step 2: Now, identify the common factors of them Common factors of 36 and 51: 1, 3.
Step 3: Choose the largest factor The largest factor that both numbers have is 3.
The GCF of 36 and 51 is 3.
GCF of 36 and 51 Using Prime Factorization
To find the GCF of 36 and 51 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 51: 51 = 3 x 17
Step 2: Now, identify the common prime factors The common prime factor is: 3
Step 3: Multiply the common prime factor 3 = 3.
The Greatest Common Factor of 36 and 51 is 3.
GCF of 36 and 51 Using Division Method or Euclidean Algorithm Method
Find the GCF of 36 and 51 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 51 by 36 51 ÷ 36 = 1 (quotient),
The remainder is calculated as 51 − (36×1) = 15
The remainder is 15, not zero, so continue the process
Step 2: Now divide the previous divisor (36) by the previous remainder (15)
Divide 36 by 15 36 ÷ 15 = 2 (quotient), remainder = 36 − (15×2) = 6
Step 3: Now divide the previous divisor (15) by the previous remainder (6)
Divide 15 by 6 15 ÷ 6 = 2 (quotient), remainder = 15 − (6×2) = 3
Step 4: Now divide the previous divisor (6) by the previous remainder (3)
Divide 6 by 3 6 ÷ 3 = 2 (quotient), remainder = 6 − (3×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 36 and 51 is 3.
Common Mistakes and How to Avoid Them in GCF of 36 and 51
Finding the GCF of 36 and 51 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 51, 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 indicates an 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; 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 51 Examples
Problem 1
A library has 36 fiction books and 51 nonfiction books. They want to organize them into the largest possible groups with the same number of books in each. How many books will be in each group?
We should find the GCF of 36 and 51 GCF of 36 and 51 3
There are 3 equal groups 36 ÷ 3 = 12 51 ÷ 3 = 17
There will be 3 groups, and each group gets 12 fiction books and 17 nonfiction books.
Explanation
As the GCF of 36 and 51 is 3, the library can make 3 groups.
\Now divide 36 and 51 by 3.
Each group gets 12 fiction books and 17 nonfiction books.
Problem 2
A conference has 36 chairs for panelists and 51 chairs for attendees. 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 36 and 51 3 So each row will have 3 chairs.
Explanation
There are 36 chairs for panelists and 51 chairs for attendees.
To find the total number of chairs in each row, we should find the GCF of 36 and 51.
There will be 3 chairs in each row.
Problem 3
A gardener has 36 roses and 51 tulips. She wants to plant them in rows with the same number of flowers in each row, using the longest possible row. How many flowers should be in each row?
For calculating the longest equal length, we have to calculate the GCF of 36 and 51
The GCF of 36 and 51 3
The length of each row is 3 flowers.
Explanation
For calculating the longest row of flowers, first, we need to calculate the GCF of 36 and 51, which is 3.
The length of each row of flowers will be 3.
Problem 4
A carpenter has two wooden planks, one 36 cm long and the other 51 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 51 3
The longest length of each piece is 3 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 36 cm and 51 cm, respectively, we have to find the GCF of 36 and 51, which is 3 cm.
The longest length of each piece is 3 cm.
Problem 5
If the GCF of 36 and ‘b’ is 3, and the LCM is 612, find ‘b’.
The value of ‘b’ is 51.
Explanation
GCF x LCM = product of the numbers
3 × 612 = 36 × b
1836 = 36b
b = 1836 ÷ 36 = 51
FAQs on the Greatest Common Factor of 36 and 51
1.What is the LCM of 36 and 51?
2.Is 36 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 51?
5.Are 36 and 51 prime numbers?
Important Glossaries for GCF of 36 and 51
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 18 are 1, 2, 3, 6, 9, and 18.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 3 are 3, 6, 9, 12, 15, 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 51 are 3 and 17.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 14 is divided by 5, the remainder is 4 and the quotient is 2.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 36 and 51 is 612.
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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.
