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102 LearnersLast updated on September 10, 2025
GCF of 32 and 80
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 32 and 80.
What is the GCF of 32 and 80?
The greatest common factor of 32 and 80 is 16. 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.
How to find the GCF of 32 and 80?
To find the GCF of 32 and 80, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 32 and 80 by Using Listing of Factors
Steps to find the GCF of 32 and 80 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 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80.
Step 2: Now, identify the common factors of them Common factors of 32 and 80: 1, 2, 4, 8, 16.
Step 3: Choose the largest factor The largest factor that both numbers have is 16. The GCF of 32 and 80 is 16.
GCF of 32 and 80 Using Prime Factorization
To find the GCF of 32 and 80 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 32: 32 = 2 x 2 x 2 x 2 x 2 = 25
Prime Factors of 80: 80 = 2 x 2 x 2 x 2 x 5 = 24 x 5
Step 2: Now, identify the common prime factors The common prime factors are: 2 x 2 x 2 x 2 = 24
Step 3: Multiply the common prime factors 24 = 16.
The Greatest Common Factor of 32 and 80 is 16.
GCF of 32 and 80 Using Division Method or Euclidean Algorithm Method
Find the GCF of 32 and 80 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 80 by 32 80 ÷ 32 = 2 (quotient), The remainder is calculated as 80 − (32×2) = 16 The remainder is 16, not zero, so continue the process
Step 2: Now divide the previous divisor (32) by the previous remainder (16) Divide 32 by 16 32 ÷ 16 = 2 (quotient), remainder = 32 − (16×2) = 0 The remainder is zero, the divisor will become the GCF.
The GCF of 32 and 80 is 16.
Common Mistakes and How to Avoid Them in GCF of 32 and 80
Finding GCF of 32 and 80 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 6, 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. However, it does not affect the GCF, but it tells about the incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples Instead of Factors
Students confuse between factors and 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 that 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 80 Examples
Problem 1
A gardener has 32 tulips and 80 roses. She wants to plant them in equal groups, with the largest number of flowers in each group. How many flowers will be in each group?
We should find the GCF of 32 and 80 GCF of 32 and 80 2^4 = 16. There are 16 equal groups 32 ÷ 16 = 2 80 ÷ 16 = 5
There will be 16 groups, and each group gets 2 tulips and 5 roses.
Explanation
As the GCF of 32 and 80 is 16, the gardener can make 16 groups. Now divide 32 and 80 by 16. Each group gets 2 tulips and 5 roses.
Problem 2
A library has 32 fiction books and 80 non-fiction books. They want to arrange them in rows with the same number of books in each row, using the largest possible number of books per row. How many books will be in each row?
GCF of 32 and 80 24 = 16. So each row will have 16 books.
Explanation
There are 32 fiction and 80 non-fiction books. To find the total number of books in each row, we should find the GCF of 32 and 80. There will be 16 books in each row.
Problem 3
A seamstress has 32 meters of cotton fabric and 80 meters of silk 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 80
The GCF of 32 and 80 24 = 16.
The fabric pieces are 16 meters long.
Explanation
For calculating the longest length of the fabric first we need to calculate the GCF of 32 and 80 which is 16. The length of each piece of fabric will be 16 meters.
Problem 4
A carpenter has two wooden planks, one 32 cm long and the other 80 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 80 24 = 16.
The longest length of each piece is 16 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 32 cm and 80 cm, respectively. We have to find the GCF of 32 and 80, which is 16 cm. The longest length of each piece is 16 cm.
Problem 5
If the GCF of 32 and ‘b’ is 16, and the LCM is 160. Find ‘b’.
The value of ‘b’ is 80.
Explanation
GCF x LCM = product of the numbers
16 × 160 = 32 × b
2560 = 32b
b = 2560 ÷ 32 = 80
FAQs on the Greatest Common Factor of 32 and 80
1.What is the LCM of 32 and 80?
2.Is 32 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 80?
5.Are 32 and 80 prime numbers?
Important Glossaries for GCF of 32 and 80
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 16 are 1, 2, 4, 8, and 16.
- 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 20 are 2 and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 13 is divided by 4, the remainder is 1 and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 32 and 80 is 160.
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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.
