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 the items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 20 and 30.
The greatest common factor of 20 and 30 is 10. 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 20 and 30, a few methods are described below -
Steps to find the GCF of 20 and 30 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 20 = 1, 2, 4, 5, 10, 20.
Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30.
Step 2: Now, identify the common factors of them Common factors of 20 and 30: 1, 2, 5, 10.
Step 3: Choose the largest factor
The largest factor that both numbers have is 10.
The GCF of 20 and 30 is 10.
To find the GCF of 20 and 30 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 20: 20 = 2 x 2 x 5 = 2² x 5
Prime Factors of 30: 30 = 2 x 3 x 5 = 2 x 3 x 5
Step 2: Now, identify the common prime factors
The common prime factors are: 2 x 5
Step 3: Multiply the common prime factors 2 x 5 = 10.
The Greatest Common Factor of 20 and 30 is 10.
Find the GCF of 20 and 30 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 30 by 20 30 ÷ 20 = 1 (quotient),
The remainder is calculated as 30 − (20×1) = 10
The remainder is 10, not zero, so continue the process
Step 2: Now divide the previous divisor (20) by the previous remainder (10)
Divide 20 by 10 20 ÷ 10 = 2 (quotient), remainder = 20 − (10×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 20 and 30 is 10.
Finding GCF of 20 and 30 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 20 apples and 30 oranges. She wants to create fruit baskets with the largest possible equal number of fruits in each basket. How many fruits will be in each basket?
We should find the GCF of 20 and 30 GCF of 20 and 30 2 x 5 = 10.
There are 10 equal baskets 20 ÷ 10 = 2 30 ÷ 10 = 3
There will be 10 baskets, and each basket gets 2 apples and 3 oranges.
As the GCF of 20 and 30 is 10, the chef can make 10 baskets.
Now divide 20 and 30 by 10.
Each basket gets 2 apples and 3 oranges.
A gardener has 20 rose plants and 30 tulip plants. They want to arrange them in rows with the same number of plants in each row, using the largest possible number of plants per row. How many plants will be in each row?
GCF of 20 and 30 2 x 5 = 10. So each row will have 10 plants.
There are 20 rose and 30 tulip plants.
To find the total number of plants in each row, we should find the GCF of 20 and 30.
There will be 10 plants in each row.
A tailor has 20 meters of blue fabric and 30 meters of red fabric. She wants to cut both fabrics 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 20 and 30
The GCF of 20 and 30 2 x 5 = 10.
The fabric is 10 meters long.
For calculating the longest length of the fabric first, we need to calculate the GCF of 20 and 30, which is 10.
The length of each piece of the fabric will be 10 meters.
A carpenter has two wooden planks, one 20 cm long and the other 30 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 20 and 30 2 x 5 = 10.
The longest length of each piece is 10 cm.
To find the longest length of each piece of the two wooden planks, 20 cm and 30 cm, respectively.
We have to find the GCF of 20 and 30, which is 10 cm.
The longest length of each piece is 10 cm.
If the GCF of 20 and ‘b’ is 10, and the LCM is 60. Find ‘b’.
The value of ‘b’ is 30.
GCF x LCM = product of the numbers 10 × 60 = 20 × b
600 = 20b
b = 600 ÷ 20 = 30
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.