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104 LearnersLast updated on September 24, 2025
GCF of 32 and 60
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 32 and 60.
What is the GCF of 32 and 60?
The greatest common factor of 32 and 60 is 4. The largest divisor of two or more numbers is called the GCF of the numbers. If two numbers are coprime, 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.
How to find the GCF of 32 and 60?
To find the GCF of 32 and 60, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 32 and 60 by Using Listing of factors
Steps to find the GCF of 32 and 60 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 32 = 1, 2, 4, 8, 16, 32.
Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Step 2: Now, identify the common factors of them Common factors of 32 and 60: 1, 2, 4.
Step 3: Choose the largest factor The largest factor that both numbers have is 4.
The GCF of 32 and 60 is 4.
GCF of 32 and 60 Using Prime Factorization
To find the GCF of 32 and 60 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 32: 32 = 2 × 2 × 2 × 2 × 2 = 25
Prime Factors of 60: 60 = 2 × 2 × 3 × 5 = 22 × 3 × 5
Step 2: Now, identify the common prime factors The common prime factors are: 2 × 2 = 22
Step 3: Multiply the common prime factors 22 = 4.
The Greatest Common Factor of 32 and 60 is 4.
GCF of 32 and 60 Using Division Method or Euclidean Algorithm Method
Find the GCF of 32 and 60 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 60 by 32 60 ÷ 32 = 1 (quotient),
The remainder is calculated as 60 − (32×1) = 28
The remainder is 28, not zero, so continue the process
Step 2: Now divide the previous divisor (32) by the previous remainder (28)
Divide 32 by 28 32 ÷ 28 = 1 (quotient), remainder = 32 − (28×1) = 4
Step 3: Now divide the previous divisor (28) by the remainder (4) 28 ÷ 4 = 7 (quotient), remainder = 28 − (4×7) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 32 and 60 is 4.
Common Mistakes and How to Avoid Them in GCF of 32 and 60
Finding GCF of 32 and 60 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
Mistake 1
Listing Incorrect Factors
Students may sometimes list incorrect factors.
For example, while listing factors of 32, students may mention 10, which is incorrect. To avoid this, students should carefully divide the number and list the factors correctly.
Mistake 2
Choosing the wrong common factor
Students may sometimes select the smallest common factor instead of the largest one. To avoid this confusion, students should list all the common factors and find the greatest one.
Mistake 3
Forgetting to include 1 as a factor
Sometimes students may forget 1 as a common factor of the numbers. Although it does not affect the GCF, it indicates an incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples instead of factors
Students confuse factors with multiples. In that confusion, sometimes they may write multiples instead of factors. To avoid this confusion, students should know the definitions of multiples and factors clearly.
Mistake 5
Assuming GCF is always an even number
Students may assume that the GCF of two numbers will always be an even number. But it's not true; a GCF can also be an odd number. To avoid this, students should focus on common factors rather than focusing on even and odd numbers.
Greatest Common Factor of 32 and 60 Examples
Problem 1
A gardener has 32 rose bushes and 60 sunflower plants. She wants to arrange them in rows with the largest possible equal number of plants in each row. How many plants will be in each row?
We should find the GCF of 32 and 60 GCF of 32 and 60 22 = 4.
There are 4 equal groups 32 ÷ 4 = 8 60 ÷ 4 = 15
There will be 4 rows, and each row gets 8 rose bushes and 15 sunflower plants.
Explanation
As the GCF of 32 and 60 is 4, the gardener can make 4 rows.
Now divide 32 and 60 by 4.
Each row gets 8 rose bushes and 15 sunflower plants.
Problem 2
A chef has 32 apples and 60 oranges. He wants to pack them into baskets with the same number of fruits in each basket, using the largest number of fruits per basket possible. How many fruits will be in each basket?
GCF of 32 and 60 22 = 4.
So each basket will have 4 fruits.
Explanation
There are 32 apples and 60 oranges.
To find the total number of fruits in each basket, we should find the GCF of 32 and 60.
There will be 4 fruits in each basket.
Problem 3
A tailor has 32 meters of green fabric and 60 meters of yellow 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 32 and 60
The GCF of 32 and 60 22 = 4.
The fabric pieces are 4 meters long.
Explanation
For calculating the longest length of the fabric pieces, first, we need to calculate the GCF of 32 and 60, which is 4.
The length of each piece of the fabric will be 4 meters.
Problem 4
A carpenter has two wooden planks, one 32 cm long and the other 60 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 32 and 60 22 = 4.
The longest length of each piece is 4 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 32 cm and 60 cm, respectively, we have to find the GCF of 32 and 60, which is 4 cm.
The longest length of each piece is 4 cm.
Problem 5
If the GCF of 32 and ‘a’ is 4, and the LCM is 480, find ‘a’.
The value of ‘a’ is 60.
Explanation
GCF × LCM = product of the numbers
4 × 480 = 32 × a
1920 = 32a
a = 1920 ÷ 32 = 60
FAQs on the Greatest Common Factor of 32 and 60
1.What is the LCM of 32 and 60?
2.Is 32 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 60?
5.Are 32 and 60 prime numbers?
Important Glossaries for GCF of 32 and 60
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 10 are 1, 2, 5, and 10.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 5 are 5, 10, 15, 20, and so on.
- Prime Factors: These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factors of 18 are 2 and 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 14 is divided by 5, the remainder is 4.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 8 and 12 is 24.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 18 and 24 will be 6, as it is their largest common factor that divides the numbers completely.
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Hiralee Lalitkumar Makwana
About the Author
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.
Fun Fact
: She loves to read number jokes and games.
