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 items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 28 and 32.
The greatest common factor of 28 and 32 is 4. 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 32, a few methods are described below:
Steps to find the GCF of 28 and 32 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 32 = 1, 2, 4, 8, 16, 32.
Step 2: Now, identify the common factors of them.
Common factors of 28 and 32: 1, 2, 4.
Step 3: Choose the largest factor.
The largest factor that both numbers have is 4.
The GCF of 28 and 32 is 4.
To find the GCF of 28 and 32 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 32: 32 = 2 x 2 x 2 x 2 x 2 = 2⁵
Step 2: Now, identify the common prime factors. The common prime factors are: 2 x 2 = 2²
Step 3: Multiply the common prime factors 2² = 4. The Greatest Common Factor of 28 and 32 is 4.
Find the GCF of 28 and 32 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number.
Here, divide 32 by 28 32 ÷ 28 = 1 (quotient),
The remainder is calculated as 32 − (28×1) = 4
The remainder is 4, not zero, so continue the process
Step 2: Now divide the previous divisor (28) by the previous remainder (4)
Divide 28 by 4 28 ÷ 4 = 7 (quotient), remainder = 28 − (4×7) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 28 and 32 is 4.
Finding the GCF of 28 and 32 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
A farmer has 28 apples and 32 oranges. He wants to pack them into the largest possible equal-sized boxes. How many items will be in each box?
We should find the GCF of 28 and 32 GCF of 28 and 32
2² = 4.
There are 4 equal boxes
28 ÷ 4 = 7
32 ÷ 4 = 8
There will be 4 boxes, and each box gets 7 apples and 8 oranges.
As the GCF of 28 and 32 is 4, the farmer can make 4 boxes.
Now divide 28 and 32 by 4.
Each box gets 7 apples and 8 oranges.
A decorator has 28 red balloons and 32 blue balloons. She wants to arrange them in rows with the same number of balloons in each row, using the largest possible number of balloons per row. How many balloons will be in each row?
GCF of 28 and 32 2² = 4. So each row will have 4 balloons.
There are 28 red and 32 blue balloons.
To find the total number of balloons in each row, we should find the GCF of 28 and 32.
There will be 4 balloons in each row.
A chef has 28 meters of yellow ribbon and 32 meters of green 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 32
The GCF of 28 and 32
2² = 4.
The ribbon is 4 meters long.
For calculating the longest length of the ribbon, first we need to calculate the GCF of 28 and 32, which is 4. The length of each piece of the ribbon will be 4 meters.
A carpenter has two wooden planks, one 28 cm long and the other 32 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 32
2² = 4.
The longest length of each piece is 4 cm.
To find the longest length of each piece of the two wooden planks, 28 cm and 32 cm, respectively, we have to find the GCF of 28 and 32, which is 4 cm. The longest length of each piece is 4 cm.
If the GCF of 28 and ‘a’ is 4, and the LCM is 224. Find ‘a’.
The value of ‘a’ is 32.
GCF x LCM = product of the numbers
4 × 224 = 28 × a
896 = 28a
a = 896 ÷ 28 = 32
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.