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100 LearnersLast updated on September 10, 2025
GCF of 32 and 81
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 32 and 81.
What is the GCF of 32 and 81?
The greatest common factor of 32 and 81 is 1. 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.
How to find the GCF of 32 and 81?
To find the GCF of 32 and 81, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 32 and 81 by Using Listing of Factors
Steps to find the GCF of 32 and 81 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 81 = 1, 3, 9, 27, 81.
Step 2: Now, identify the common factors of them Common factors of 32 and 81: 1.
Step 3: Choose the largest factor The largest factor that both numbers have is 1. The GCF of 32 and 81 is 1.
GCF of 32 and 81 Using Prime Factorization
To find the GCF of 32 and 81 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 81: 81 = 3 x 3 x 3 x 3 = 34
Step 2: Now, identify the common prime factors There are no common prime factors.
Step 3: Since there are no common prime factors, the GCF is 1. The Greatest Common Factor of 32 and 81 is 1.
GCF of 32 and 81 Using Division Method or Euclidean Algorithm Method
Find the GCF of 32 and 81 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 81 by 32 81 ÷ 32 = 2 (quotient), The remainder is calculated as 81 − (32×2) = 17
The remainder is 17, not zero, so continue the process
Step 2: Now divide the previous divisor (32) by the previous remainder (17) Divide 32 by 17 32 ÷ 17 = 1 (quotient), remainder = 32 − (17×1) = 15
Step 3: Continue the process Divide 17 by 15 17 ÷ 15 = 1 (quotient), remainder = 17 − (15×1) = 2
Step 4: Continue the process Divide 15 by 2 15 ÷ 2 = 7 (quotient), remainder = 15 − (2×7) = 1
Step 5: Continue the process Divide 2 by 1 2 ÷ 1 = 2 (quotient), remainder = 2 − (1×2) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 32 and 81 is 1.
Common Mistakes and How to Avoid Them in GCF of 32 and 81
Finding GCF of 32 and 81 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 a non-common factor instead of the correct 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. This does not affect the GCF, but 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 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 greater than 1
Students may assume that the GCF of two numbers will always be greater than 1. But if two numbers are co-prime, their GCF is 1. To avoid this, students should focus on finding common factors rather than making assumptions.
Greatest Common Factor of 32 and 81 Examples
Problem 1
A baker has 32 chocolate cookies and 81 vanilla cookies. He wants to pack them into bags with equal numbers of cookies in each bag, using the greatest number of bags possible. How many cookies will be in each bag?
We should find the GCF of 32 and 81. The GCF of 32 and 81 is 1. There will be 1 cookie of each type in each bag.
Explanation
As the GCF of 32 and 81 is 1, each bag will contain 1 cookie of each type.
Problem 2
A gardener has 32 rose plants and 81 tulip plants. She wants to plant them in rows with the same number of plants in each row, using the largest possible number of plants per row. How many plants will be in each row?
GCF of 32 and 81 is 1. So each row will have 1 plant of each type.
Explanation
There are 32 rose plants and 81 tulip plants. To find the total number of plants in each row, we should find the GCF of 32 and 81. There will be 1 plant of each type in each row.
Problem 3
A tailor has 32 meters of blue fabric and 81 meters of green 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 81. The GCF of 32 and 81 is 1. The length of each piece is 1 meter.
Explanation
For calculating the longest length of the fabric, first, we need to calculate the GCF of 32 and 81, which is 1. The length of each piece of fabric will be 1 meter.
Problem 4
A carpenter has two wooden planks, one 32 cm long and the other 81 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. The GCF of 32 and 81 is 1. The longest length of each piece is 1 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 32 cm and 81 cm, respectively, we have to find the GCF of 32 and 81, which is 1 cm. The longest length of each piece is 1 cm.
Problem 5
If the GCF of 32 and ‘a’ is 1, and the LCM is 2592. Find ‘a’.
The value of ‘a’ is 81.
Explanation
GCF x LCM = product of the numbers 1 × 2592 = 32 × a 2592 = 32a a = 2592 ÷ 32 = 81
FAQs on the Greatest Common Factor of 32 and 81
1.What is the LCM of 32 and 81?
2.Is 32 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 81?
5.Are 32 and 81 prime numbers?
Important Glossaries for GCF of 32 and 81
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 32 are 1, 2, 4, 8, 16, and 32.
- 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 81 are 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 3, 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 81 is 2592.
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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.
