102 LearnersLast updated on August 5th, 2025
GCF of 30 and 225
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 to schedule events. In this topic, we will learn about the GCF of 30 and 225.
What is the GCF of 30 and 225?
The greatest common factor of 30 and 225 is 15. 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 30 and 225?
To find the GCF of 30 and 225, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 30 and 225 by Using Listing of factors
Steps to find the GCF of 30 and 225 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 225 = 1, 3, 5, 9, 15, 25, 45, 75, 225.
Step 2: Now, identify the common factors of them
Common factors of 30 and 225: 1, 3, 5, 15.
Step 3: Choose the largest factor
The largest factor that both numbers have is 15.
The GCF of 30 and 225 is 15.
GCF of 30 and 225 Using Prime Factorization
To find the GCF of 30 and 225 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 30: 30 = 2 × 3 × 5
Prime Factors of 225: 225 = 3 × 3 × 5 × 5 = 3² × 5²
Step 2: Now, identify the common prime factors
The common prime factors are: 3 × 5
Step 3: Multiply the common prime factors 3 × 5 = 15.
The Greatest Common Factor of 30 and 225 is 15.
GCF of 30 and 225 Using Division Method or Euclidean Algorithm Method
Find the GCF of 30 and 225 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 225 by 30 225 ÷ 30 = 7 (quotient),
The remainder is calculated as 225 − (30×7) = 15.
The remainder is 15, not zero, so continue the process
Step 2: Now divide the previous divisor (30) by the previous remainder (15)
Divide 30 by 15 30 ÷ 15 = 2 (quotient), remainder = 30 − (15×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 30 and 225 is 15.
Common Mistakes and How to Avoid Them in GCF of 30 and 225
Finding the GCF of 30 and 225 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 225 Examples
Problem 1
A chef has 30 apples and 225 strawberries. She wants to pack them into fruit baskets with the largest number of fruits in each basket. How many fruits will be in each basket?
We should find the GCF of 30 and 225 GCF of 30 and 225 3 × 5 = 15. There are 15 fruits in each basket. 30 ÷ 15 = 2 225 ÷ 15 = 15 There will be 15 baskets, and each basket gets 2 apples and 15 strawberries.
Explanation
As the GCF of 30 and 225 is 15, the chef can make 15 baskets.
Now divide 30 and 225 by 15.
Each basket gets 2 apples and 15 strawberries.
Problem 2
A painter has 30 red paint cans and 225 blue paint cans. He wants to arrange them in stacks with the same number of cans in each stack, using the largest possible number of cans per stack. How many cans will be in each stack?
GCF of 30 and 225 3 × 5 = 15. So each stack will have 15 cans.
Explanation
There are 30 red and 225 blue paint cans.
To find the total number of cans in each stack, we should find the GCF of 30 and 225.
There will be 15 cans in each stack.
Problem 3
A florist has 30 meters of red ribbon and 225 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 30 and 225. The GCF of 30 and 225 3 × 5 = 15. The ribbon is 15 meters long.
Explanation
For calculating the longest length of the ribbon, first, we need to calculate the GCF of 30 and 225, which is 15.
The length of each piece of the ribbon will be 15 meters.
Problem 4
A builder has two wooden beams, one 30 cm long and the other 225 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 builder needs the longest piece of wood GCF of 30 and 225 3 × 5 = 15. The longest length of each piece is 15 cm.
Explanation
To find the longest length of each piece of the two wooden beams, 30 cm and 225 cm, respectively, we have to find the GCF of 30 and 225, which is 15 cm.
The longest length of each piece is 15 cm.
Problem 5
If the GCF of 30 and ‘b’ is 15, and the LCM is 450, find ‘b’.
The value of ‘b’ is 225.
Explanation
GCF × LCM = product of the numbers
15 × 450 = 30 × b
6750 = 30b
b = 6750 ÷ 30 = 225
FAQs on the Greatest Common Factor of 30 and 225
1.What is the LCM of 30 and 225?
2.Is 30 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 225?
5.Are 30 and 225 prime numbers?
6.How can children in Canada use numbers in everyday life to understand GCF of 30 and 225?
7.What are some fun ways kids in Canada can practice GCF of 30 and 225 with numbers?
8.What role do numbers and GCF of 30 and 225 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve GCF of 30 and 225 skills?
Important Glossaries for GCF of 30 and 225
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 15 are 1, 3, 5, and 15.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 5 are 5, 10, 15, 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 30 are 2, 3, and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 20 is divided by 6, the remainder is 2 and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 30 and 225 is 450.
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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.
