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 to schedule events. In this topic, we will learn about the GCF of 18 and 28.
The greatest common factor of 18 and 28 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 18 and 28, a few methods are described below:
Steps to find the GCF of 18 and 28 using the listing of factors:
Step 1: Firstly, list the factors of each number:
Factors of 18 = 1, 2, 3, 6, 9, 18.
Factors of 28 = 1, 2, 4, 7, 14, 28.
Step 2: Now, identify the common factors of them. Common factors of 18 and 28: 1, 2.
Step 3: Choose the largest factor. The largest factor that both numbers have is 2.
The GCF of 18 and 28 is 2.
To find the GCF of 18 and 28 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number.
Prime Factors of 18: 18 = 2 × 3 × 3 = 2 × 3²
Prime Factors of 28: 28 = 2 × 2 × 7 = 2² × 7
Step 2: Now, identify the common prime factors. The common prime factor is: 2
Step 3: Multiply the common prime factors 2 = 2.
The Greatest Common Factor of 18 and 28 is 2.
Find the GCF of 18 and 28 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 28 by 18 28 ÷ 18 = 1 (quotient), The remainder is calculated as 28 − (18×1) = 10
The remainder is 10, not zero, so continue the process
Step 2: Now divide the previous divisor (18) by the previous remainder (10) 18 ÷ 10 = 1 (quotient), remainder = 18 − (10×1) = 8
Step 3: Now continue with the remainder 10 ÷ 8 = 1 (quotient), remainder = 10 − (8×1) = 2
Step 4: Now divide the previous divisor (8) by the previous remainder (2) 8 ÷ 2 = 4 (quotient), remainder = 8 − (2×4) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 18 and 28 is 2.
Finding GCF of 18 and 28 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 18 tulips and 28 daisies. She wants to plant them in equal groups, with the largest number of plants in each group. How many plants will be in each group?
We should find the GCF of 18 and 28 GCF of 18 and 28 2.
There are 2 equal groups
18 ÷ 2 = 9
28 ÷ 2 = 14
There will be 2 groups, and each group gets 9 tulips and 14 daisies.
As the GCF of 18 and 28 is 2, the gardener can make 2 groups.
Now divide 18 and 28 by 2.
Each group gets 9 tulips and 14 daisies.
A bakery has 18 chocolate cupcakes and 28 vanilla cupcakes. They want to arrange them in trays with the same number of cupcakes in each tray, using the largest possible number of cupcakes per tray. How many cupcakes will be in each tray?
GCF of 18 and 28 2. So each tray will have 2 cupcakes.
There are 18 chocolate and 28 vanilla cupcakes.
To find the total number of cupcakes in each tray, we should find the GCF of 18 and 28.
There will be 2 cupcakes in each tray.
A tailor has 18 meters of red fabric and 28 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 the longest equal length, we have to calculate the GCF of 18 and 28
The GCF of 18 and 28 2.
The fabric is 2 meters long.
For calculating the longest length of the fabric first we need to calculate the GCF of 18 and 28 which is 2.
The length of each piece of the fabric will be 2 meters.
A carpenter has two wooden planks, one 18 cm long and the other 28 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 18 and 28 2.
The longest length of each piece is 2 cm.
To find the longest length of each piece of the two wooden planks, 18 cm and 28 cm, respectively. We have to find the GCF of 18 and 28, which is 2 cm. The longest length of each piece is 2 cm.
If the GCF of 18 and ‘b’ is 2, and the LCM is 252, find ‘b’.
The value of ‘b’ is 28.
GCF × LCM = product of the numbers
2 × 252 = 18 × b
504 = 18b
b = 504 ÷ 18 = 28
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.