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 to schedule events. In this topic, we will learn about the GCF of 54 and 32.
The greatest common factor of 54 and 32 is 2. The largest divisor of two or more numbers is called the GCF of the numbers. 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 54 and 32, a few methods are described below:
Steps to find the GCF of 54 and 32 using the listing of factors:
Step 1: Firstly, list the factors of each number:
Factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54.
Factors of 32 = 1, 2, 4, 8, 16, 32.
Step 2: Now, identify the common factors of them. Common factors of 54 and 32: 1, 2.
Step 3: Choose the largest factor:
The largest factor that both numbers have is 2.
The GCF of 54 and 32 is 2.
To find the GCF of 54 and 32 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime:
Factors of 54: 54 = 2 x 3 x 3 x 3 = 2 x 3³
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
Step 3: Multiply the common prime factors. The Greatest Common Factor of 54 and 32 is 2.
Find the GCF of 54 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 54 by 32 54 ÷ 32 = 1 (quotient), The remainder is calculated as 54 − (32×1) = 22
The remainder is 22, not zero, so continue the process
Step 2: Now divide the previous divisor (32) by the previous remainder (22) 32 ÷ 22 = 1 (quotient), remainder = 32 − (22×1) = 10
Step 3: Continue the process 22 ÷ 10 = 2 (quotient), remainder = 22 − (10×2) = 2 10 ÷ 2 = 5 (quotient), remainder = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 54 and 32 is 2.
Finding the GCF of 54 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 54 apples and 32 oranges. He wants to pack them into the largest possible number of boxes, with an equal number of apples and oranges in each box. How many apples and oranges will be in each box?
We should find the GCF of 54 and 32.
GCF of 54 and 32 is 2.
54 ÷ 2 = 27
32 ÷ 2 = 16
There will be 2 boxes, and each box gets 27 apples and 16 oranges.
As the GCF of 54 and 32 is 2, the farmer can make 2 boxes.
Now divide 54 and 32 by 2.
Each box gets 27 apples and 16 oranges.
A company has 54 laptops and 32 tablets. It wants to distribute them equally among its branches, with the largest possible number of devices per branch. How many devices will each branch receive?
GCF of 54 and 32 is 2. So each branch will have 2 devices.
There are 54 laptops and 32 tablets.
To find the total number of devices in each branch, we should find the GCF of 54 and 32.
There will be 2 devices in each branch.
A cook has 54 ounces of flour and 32 ounces of sugar. She wants to pack them into bags of equal weight, using the largest possible weight per bag. What should be the weight of each bag?
For calculating the largest equal weight, we have to calculate the GCF of 54 and 32.
The GCF of 54 and 32 is 2.
Each bag will weigh 2 ounces.
For calculating the largest weight of the bags, first, we need to calculate the GCF of 54 and 32 which is 2. The weight of each bag will be 2 ounces.
A gardener has two plots of land, one 54 meters long and the other 32 meters long. He wants to divide them into the longest possible equal sections, without any land left over. What should be the length of each section?
The gardener needs the longest section of land. GCF of 54 and 32 is 2. The longest length of each section is 2 meters.
To find the longest length of each section of the two plots of land, 54 meters and 32 meters, respectively, we have to find the GCF of 54 and 32, which is 2 meters. The longest length of each section is 2 meters.
If the GCF of 54 and ‘a’ is 6, and the LCM is 288. Find ‘a’.
The value of ‘a’ is 32.
GCF x LCM = product of the numbers
6 × 288 = 54 × a
1728 = 54a
a = 1728 ÷ 54 = 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.