Last updated on August 5th, 2025
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.
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.
To find the GCF of 30 and 225, a few methods are described below -
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
If the GCF of 30 and ‘b’ is 15, and the LCM is 450, find ‘b’.
The value of ‘b’ is 225.
GCF × LCM = product of the numbers
15 × 450 = 30 × b
6750 = 30b
b = 6750 ÷ 30 = 225
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.
: She loves to read number jokes and games.