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102 LearnersLast updated on September 18, 2025
GCF of 30 and 36
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 30 and 36.
What is the GCF of 30 and 36?
The greatest common factor of 30 and 36 is 6. 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 all divisors are positive.
How to find the GCF of 30 and 36?
To find the GCF of 30 and 36, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 30 and 36 by Using Listing of Factors
Steps to find the GCF of 30 and 36 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30.
Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36.
Step 2: Now, identify the common factors of them Common factors of 30 and 36: 1, 2, 3, 6.
Step 3: Choose the largest factor The largest factor that both numbers have is 6. The GCF of 30 and 36 is 6.
GCF of 30 and 36 Using Prime Factorization
To find the GCF of 30 and 36 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 30: 30 = 2 x 3 x 5
Prime Factors of 36: 36 = 2 x 2 x 3 x 3
Step 2: Now, identify the common prime factors The common prime factors are: 2 x 3
Step 3: Multiply the common prime factors 2 x 3 = 6. The Greatest Common Factor of 30 and 36 is 6.
GCF of 30 and 36 Using Division Method or Euclidean Algorithm Method
Find the GCF of 30 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 30 36 ÷ 30 = 1 (quotient),
The remainder is calculated as 36 − (30×1) = 6
The remainder is 6, not zero, so continue the process
Step 2: Now divide the previous divisor (30) by the previous remainder (6)
Divide 30 by 6 30 ÷ 6 = 5 (quotient), remainder = 30 − (6×5) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 30 and 36 is 6.
Common Mistakes and How to Avoid Them in GCF of 30 and 36
Finding the GCF of 30 and 36 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 30, students may mention 8, 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 30 and 36 Examples
Problem 1
A baker has 30 cupcakes and 36 cookies. She wants to pack them into equal boxes, with the largest number of items in each box. How many items will be in each box?
We should find the GCF of 30 and 36 GCF of 30 and 36 2 x 3 = 6.
There are 6 items in each box. 30 ÷ 6 = 5 36 ÷ 6 = 6
There will be 6 boxes, and each box gets 5 cupcakes and 6 cookies.
Explanation
As the GCF of 30 and 36 is 6, the baker can make 6 boxes.
Now divide 30 and 36 by 6.
Each box gets 5 cupcakes and 6 cookies.
Problem 2
A concert has 30 musicians and 36 singers. They want to arrange them in rows with the same number of people in each row, using the largest possible number of people per row. How many people will be in each row?
GCF of 30 and 36 2 x 3 = 6. So each row will have 6 people.
Explanation
There are 30 musicians and 36 singers.
To find the total number of people in each row, we should find the GCF of 30 and 36.
There will be 6 people in each row.
Problem 3
A florist has 30 red roses and 36 white roses. She wants to arrange them in bouquets of equal size, using the largest possible number of roses in each bouquet. What should be the size of each bouquet?
For calculating the largest equal size, we have to calculate the GCF of 30 and 36
The GCF of 30 and 36 2 x 3 = 6.
Each bouquet will have 6 roses.
Explanation
For calculating the largest bouquet size, first, we need to calculate the GCF of 30 and 36, which is 6.
The size of each bouquet will be 6 roses.
Problem 4
A tailor has two rolls of fabric, one 30 meters long and the other 36 meters long. She wants to cut them into the longest possible equal pieces, without any fabric left over. What should be the length of each piece?
The tailor needs the longest piece of fabric GCF of 30 and 36 2 x 3 = 6.
The longest length of each piece is 6 meters.
Explanation
To find the longest length of each piece of the two fabric rolls, 30 meters and 36 meters, respectively.
We have to find the GCF of 30 and 36, which is 6 meters.
The longest length of each piece is 6 meters.
Problem 5
If the GCF of 30 and ‘a’ is 6, and the LCM is 180, find ‘a’.
The value of ‘a’ is 36.
Explanation
GCF x LCM = product of the numbers
6 x 180 = 30 x a
1080 = 30a
a = 1080 ÷ 30 = 36
FAQs on the Greatest Common Factor of 30 and 36
1.What is the LCM of 30 and 36?
2.Is 30 divisible by 5?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 36?
5.Are 30 and 36 prime numbers?
Important Glossaries for GCF of 30 and 36
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 4 are 4, 8, 12, 16, 20, 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 15 are 3 and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 12 is divided by 7, the remainder is 5 and the quotient is 1.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 30 and 36 is 180.
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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.
