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101 LearnersLast updated on September 23, 2025
GCF of 32 and 64
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 64.
What is the GCF of 32 and 64?
The greatest common factor of 32 and 64 is 32.
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 64?
To find the GCF of 32 and 64, a few methods are described below -
Listing Factors Prime Factorization Long Division Method / by Euclidean Algorithm
GCF of 32 and 64 by Using Listing of factors
Steps to find the GCF of 32 and 64 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 64 = 1, 2, 4, 8, 16, 32, 64.
Step 2: Now, identify the common factors of them Common factors of 32 and 64: 1, 2, 4, 8, 16, 32.
Step 3: Choose the largest factor The largest factor that both numbers have is 32. The GCF of 32 and 64 is 32.
GCF of 32 and 64 Using Prime Factorization
To find the GCF of 32 and 64 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 = 2^5 Prime Factors of 64: 64 = 2 x 2 x 2 x 2 x 2 x 2 = 2^6.
Step 2: Now, identify the common prime factors The common prime factors are: 2 x 2 x 2 x 2 x 2 = 2^5.
Step 3: Multiply the common prime factors 2^5 = 32.
The Greatest Common Factor of 32 and 64 is 32.
GCF of 32 and 64 Using Division Method or Euclidean Algorithm Method
Find the GCF of 32 and 64 using the division method or Euclidean Algorithm Method.
Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 64 by 32 64 ÷ 32 = 2 (quotient), The remainder is calculated as 64 − (32×2) = 0 The remainder is zero, so the divisor becomes the GCF.
The GCF of 32 and 64 is 32.
Common Mistakes and How to Avoid Them in GCF of 32 and 64
Finding the GCF of 32 and 64 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.
However, it does not affect the GCF, but it indicates an incomplete understanding of the factors.
Students should include 1 as a factor.
Mistake 4
Confusing Multiples with Factors
Students often 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 64 Examples
Problem 1
A farmer has 32 apple trees and 64 orange trees. He wants to plant them in rows with the largest number of trees in each row. How many trees will be in each row?
We should find the GCF of 32 and 64 GCF of 32 and 64 2^5 = 32.
Each row will have 32 trees.
Explanation
As the GCF of 32 and 64 is 32, the farmer can plant 32 trees in each row.
Problem 2
A warehouse has 32 large boxes and 64 small boxes. They want to arrange them in stacks with the same number of boxes in each stack, using the largest possible number of boxes per stack. How many boxes will be in each stack?
GCF of 32 and 64 2^5 = 32 So each stack will have 32 boxes.
Explanation
There are 32 large and 64 small boxes.
To find the total number of boxes in each stack, we should find the GCF of 32 and 64.
There will be 32 boxes in each stack.
Problem 3
A tailor has 32 meters of cotton fabric and 64 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 64 The GCF of 32 and 64 2^5 = 32.
Each piece of fabric is 32 meters long.
Explanation
For calculating the longest length of the fabric, first we need to calculate the GCF of 32 and 64, which is 32.
The length of each piece of fabric will be 32 meters.
Problem 4
A carpenter has two wooden planks, one 32 cm long and the other 64 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 64 2^5 = 32.
The longest length of each piece is 32 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 32 cm and 64 cm, respectively, we have to find the GCF of 32 and 64, which is 32 cm.
The longest length of each piece is 32 cm.
Problem 5
If the GCF of 32 and ‘a’ is 16, and the LCM is 128. Find ‘a’.
The value of ‘a’ is 64.
Explanation
GCF x LCM = product of the numbers 16 × 128 = 32 × a 2048 = 32a a = 2048 ÷ 32 = 64
FAQs on the Greatest Common Factor of 32 and 64
1.What is the LCM of 32 and 64?
2.Is 32 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 64?
5.Are 32 and 64 prime numbers?
Important Glossaries for GCF of 32 and 64
- 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 8 are 8, 16, 24, 32, 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 64 are 2.
- 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.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 32 and 64 is 64.
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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.
