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 28 and 56.
The greatest common factor of 28 and 56 is 28. 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 28 and 56, a few methods are described below -
Steps to find the GCF of 28 and 56 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 28 = 1, 2, 4, 7, 14, 28.
Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56.
Step 2: Now, identify the common factors of them Common factors of 28 and 56: 1, 2, 4, 7, 14, 28.
Step 3: Choose the largest factor
The largest factor that both numbers have is 28.
The GCF of 28 and 56 is 28.
To find the GCF of 28 and 56 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 28: 28 = 2 x 2 x 7 = 2² x 7
Prime Factors of 56: 56 = 2 x 2 x 2 x 7 = 2³ x 7
Step 2: Now, identify the common prime factors
The common prime factors are: 2 x 2 x 7 = 2² x 7
Step 3: Multiply the common prime factors 2² x 7 = 4 x 7 = 28.
The Greatest Common Factor of 28 and 56 is 28.
Find the GCF of 28 and 56 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 56 by 28 56 ÷ 28 = 2 (quotient),
The remainder is calculated as 56 − (28×2) = 0
Since the remainder is zero, the divisor will become the GCF.
The GCF of 28 and 56 is 28.
Finding GCF of 28 and 56 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 28 tulip bulbs and 56 daffodil bulbs. She wants to plant them in rows with the largest number of bulbs in each row. How many bulbs will be in each row?
We should find the GCF of 28 and 56 GCF of 28 and 56 2² x 7 = 4 x 7 = 28.
There are 28 equal groups 28 ÷ 28 = 1 56 ÷ 28 = 2
There will be 28 groups, and each row will have 1 tulip bulb and 2 daffodil bulbs.
As the GCF of 28 and 56 is 28, the gardener can make 28 rows.
Now divide 28 and 56 by 28.
Each row gets 1 tulip bulb and 2 daffodil bulbs.
A school has 28 red chairs and 56 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?
GCF of 28 and 56 2² x 7 = 4 x 7 = 28.
So each row will have 28 chairs.
There are 28 red and 56 blue chairs.
To find the total number of chairs in each row, we should find the GCF of 28 and 56.
There will be 28 chairs in each row.
A tailor has 28 meters of red ribbon and 56 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 28 and 56
The GCF of 28 and 56
2² x 7 = 4 x 7 = 28.
The ribbon is 28 meters long.
For calculating the longest length of the ribbon, first, we need to calculate the GCF of 28 and 56, which is 28.
The length of each piece of ribbon will be 28 meters.
A carpenter has two wooden planks, one 28 cm long and the other 56 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 28 and 56 2² x 7 = 4 x 7 = 28.
The longest length of each piece is 28 cm.
To find the longest length of each piece of the two wooden planks, 28 cm and 56 cm, respectively, we have to find the GCF of 28 and 56, which is 28 cm.
The longest length of each piece is 28 cm.
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.