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101 LearnersLast updated on September 18, 2025
GCF of 30 and 48
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 48.
What is the GCF of 30 and 48?
The greatest common factor of 30 and 48 is 6. 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 48?
To find the GCF of 30 and 48, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 30 and 48 by Using Listing of factors
Steps to find the GCF of 30 and 48 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 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
Step 2: Now, identify the common factors of them Common factors of 30 and 48: 1, 2, 3, 6.
Step 3: Choose the largest factor The largest factor that both numbers have is 6. The GCF of 30 and 48 is 6.
GCF of 30 and 48 Using Prime Factorization
To find the GCF of 30 and 48 using 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 48: 48 = 2 x 2 x 2 x 2 x 3 = 24 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 48 is 6.
GCF of 30 and 48 Using Division Method or Euclidean Algorithm Method
Find the GCF of 30 and 48 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 48 by 30 48 ÷ 30 = 1 (quotient),
The remainder is calculated as 48 − (30×1) = 18
The remainder is 18, not zero, so continue the process
Step 2: Now divide the previous divisor (30) by the previous remainder (18)
Divide 30 by 18 30 ÷ 18 = 1 (quotient), remainder = 30 − (18×1) = 12
Step 3: Continue with the same process Now divide 18 by 12 18 ÷ 12 = 1 (quotient), remainder = 18 − (12×1) = 6
Step 4: Now divide 12 by 6 12 ÷ 6 = 2 (quotient), remainder = 12 − (6×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 30 and 48 is 6.
Common Mistakes and How to Avoid Them in GCF of 30 and 48
Finding GCF of 30 and 48 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 9 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 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 30 and 48 Examples
Problem 1
A gardener has 30 rose plants and 48 tulip plants. She wants to arrange them into equal rows, with the largest number of plants in each row. How many plants will be in each row?
We should find GCF of 30 and 48 GCF of 30 and 48 = 6.
There are 6 equal rows 30 ÷ 6 = 5 48 ÷ 6 = 8
There will be 6 rows, and each row gets 5 rose plants and 8 tulip plants.
Explanation
As the GCF of 30 and 48 is 6, the gardener can make 6 rows.
Now divide 30 and 48 by 6.
Each row gets 5 rose plants and 8 tulip plants.
Problem 2
A chef has 30 red apples and 48 green apples. He wants to arrange them in trays with the same number of apples in each tray, using the largest possible number of apples per tray. How many apples will be in each tray?
GCF of 30 and 48 = 6. So each tray will have 6 apples.
Explanation
There are 30 red and 48 green apples.
To find the total number of apples in each tray, we should find the GCF of 30 and 48.
There will be 6 apples in each tray.
Problem 3
A rope maker has 30 meters of nylon rope and 48 meters of cotton rope. He wants to cut both ropes into pieces of equal length, using the longest possible length. What should be the length of each piece?
For calculating longest equal length, we have to calculate the GCF of 30 and 48
The GCF of 30 and 48 = 6.
The ropes are 6 meters long.
Explanation
For calculating the longest length of the ropes, first we need to calculate the GCF of 30 and 48 which is 6.
The length of each piece of the rope will be 6 meters.
Problem 4
A carpenter has two wooden planks, one 30 cm long and the other 48 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 30 and 48 = 6.
The longest length of each piece is 6 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 30 cm and 48 cm, respectively.
We have to find the GCF of 30 and 48, which is 6 cm.
The longest length of each piece is 6 cm.
Problem 5
If the GCF of 30 and ‘b’ is 6, and the LCM is 240. Find ‘b’.
The value of ‘b’ is 48.
Explanation
GCF x LCM = product of the numbers
6 × 240 = 30 × b
1440 = 30b
b = 1440 ÷ 30 = 48
FAQs on the Greatest Common Factor of 30 and 48
1.What is the LCM of 30 and 48?
2.Is 30 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 48?
5.Are 30 and 48 prime numbers?
Important Glossaries for GCF of 30 and 48
- 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 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 20 are 2 and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 13 is divided by 5, the remainder is 3 and the quotient is 2.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 30 and 48 is 240.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 30 and 48 will be 6, 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.
