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 18.
The greatest common factor of 20 and 18 is 2. 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 18, a few methods are described below -
Steps to find the GCF of 20 and 18 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 18 = 1, 2, 3, 6, 9, 18.
Step 2: Now, identify the common factors of them Common factors of 20 and 18: 1, 2.
Step 3: Choose the largest factor
The largest factor that both numbers have is 2.
The GCF of 20 and 18 is 2.
To find the GCF of 20 and 18 using 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 18: 18 = 2 x 3 x 3 = 2 x 3²
Step 2: Now, identify the common prime factors
The common prime factor is: 2
Step 3: Multiply the common prime factors
The GCF is 2.
The Greatest Common Factor of 20 and 18 is 2.
Find the GCF of 20 and 18 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 20 by 18 20 ÷ 18 = 1 (quotient),
The remainder is calculated as 20 − (18×1) = 2
The remainder is 2, not zero, so continue the process
Step 2: Now divide the previous divisor (18) by the previous remainder (2)
Divide 18 by 2 18 ÷ 2 = 9 (quotient), remainder = 18 − (2×9) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 20 and 18 is 2.
Finding GCF of 20 and 18 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
A gardener has 20 rose plants and 18 sunflower plants. He wants to arrange them in equal rows, with the largest number of plants in each row. How many plants will be in each row?
We should find GCF of 20 and 18 GCF of 20 and 18 is 2.
There are 2 equal rows 20 ÷ 2 = 10
18 ÷ 2 = 9
There will be 2 rows, and each row gets 10 rose plants and 9 sunflower plants.
As the GCF of 20 and 18 is 2, the gardener can make 2 rows. Now divide 20 and 18 by 2. Each row gets 10 rose plants and 9 sunflower plants.
A chef has 20 apples and 18 oranges. He wants to distribute them in baskets with the same number of fruits in each basket, using the largest possible number of fruits per basket. How many fruits will be in each basket?
GCF of 20 and 18 is 2.
So each basket will have 2 fruits.
There are 20 apples and 18 oranges. To find the total number of fruits in each basket, we should find the GCF of 20 and 18. Each basket will have 2 fruits.
A tailor has 20 meters of red fabric and 18 meters of blue 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 longest equal length, we have to calculate the GCF of 20 and 18.
The GCF of 20 and 18 is 2.
The fabric pieces will be 2 meters long.
For calculating the longest length of the fabric, first we need to calculate the GCF of 20 and 18, which is 2. The length of each piece of the fabric will be 2 meters.
A carpenter has two wooden planks, one 20 cm long and the other 18 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 18 is 2.
The longest length of each piece is 2 cm.
To find the longest length of each piece of the two wooden planks, 20 cm and 18 cm, respectively, we have to find the GCF of 20 and 18, which is 2 cm. The longest length of each piece is 2 cm.
If the GCF of 20 and ‘a’ is 2, and the LCM is 180. Find ‘a’.
The value of ‘a’ is 18.
GCF x LCM = product of the numbers 2 × 180 = 20 × a
360 = 20a
a = 360 ÷ 20 = 18
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.