106 LearnersLast updated on August 5th, 2025
GCF of 12 and 32
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 12 and 32.
What is the GCF of 12 and 32?
The greatest common factor of 12 and 32 is 4. 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 12 and 32?
To find the GCF of 12 and 32, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 12 and 32 by Using Listing of Factors
Steps to find the GCF of 12 and 32 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 12 = 1, 2, 3, 4, 6, 12.
Factors of 32 = 1, 2, 4, 8, 16, 32.
Step 2: Now, identify the common factors of them Common factors of 12 and 32: 1, 2, 4.
Step 3: Choose the largest factor
The largest factor that both numbers have is 4.
The GCF of 12 and 32 is 4.
GCF of 12 and 32 Using Prime Factorization
To find the GCF of 12 and 32 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 12: 12 = 2 x 2 x 3 = 2² x 3
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 factor is: 2 x 2 = 2²
Step 3: Multiply the common prime factors 2² = 4.
The Greatest Common Factor of 12 and 32 is 4.
GCF of 12 and 32 Using Division Method or Euclidean Algorithm Method
Find the GCF of 12 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 32 by 12 32 ÷ 12 = 2 (quotient),
The remainder is calculated as 32 − (12×2) = 8
The remainder is 8, not zero, so continue the process
Step 2: Now divide the previous divisor (12) by the previous remainder (8)
Divide 12 by 8 12 ÷ 8 = 1 (quotient), remainder = 12 − (8×1) = 4
Step 3: Now divide the previous divisor (8) by the previous remainder (4) 8 ÷ 4 = 2 (quotient), remainder = 8 − (4×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 12 and 32 is 4.
Common Mistakes and How to Avoid Them in GCF of 12 and 32
Finding GCF of 12 and 32 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 12, 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
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 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 12 and 32 Examples
Problem 1
A gardener has 12 red flowers and 32 yellow flowers. She wants to arrange them in bouquets with an equal number of flowers, using the largest possible number of flowers per bouquet. How many flowers will be in each bouquet?
We should find the GCF of 12 and 32. GCF of 12 and 32 2² = 4.
There are 4 bouquets. 12 ÷ 4 = 3 32 ÷ 4 = 8
There will be 4 bouquets, and each bouquet gets 3 red flowers and 8 yellow flowers.
Explanation
As the GCF of 12 and 32 is 4, the gardener can make 4 bouquets. Now divide 12 and 32 by 4. Each bouquet gets 3 red flowers and 8 yellow flowers.
Problem 2
A chef has 12 small plates and 32 large plates. He wants to arrange them in stacks with the same number of plates, using the largest possible number of plates per stack. How many plates will be in each stack?
GCF of 12 and 32 2² = 4.
So each stack will have 4 plates.
Explanation
There are 12 small plates and 32 large plates. To find the total number of plates in each stack, we should find the GCF of 12 and 32. There will be 4 plates in each stack.
Problem 3
A painter has 12 meters of red paint tape and 32 meters of blue paint tape. He wants to cut both tapes 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 12 and 32.
The GCF of 12 and 32 2² = 4.
The tape is 4 meters long.
Explanation
For calculating the longest length of the tape, first, we need to calculate the GCF of 12 and 32, which is 4. The length of each piece of the tape will be 4 meters.
Problem 4
A carpenter has two wooden planks, one 12 cm long and the other 32 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 12 and 32 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, 12 cm and 32 cm, respectively, we have to find the GCF of 12 and 32, which is 4 cm. The longest length of each piece is 4 cm.
Problem 5
If the GCF of 12 and ‘b’ is 4, and the LCM is 96, find ‘b’.
The value of ‘b’ is 32.
Explanation
GCF x LCM = product of the numbers 4 × 96 = 12 × b
384 = 12b
b = 384 ÷ 12 = 32
FAQs on the Greatest Common Factor of 12 and 32
1.What is the LCM of 12 and 32?
2.Is 12 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 32?
5.Are 12 and 32 prime numbers?
6.How can children in United States use numbers in everyday life to understand GCF of 12 and 32?
7.What are some fun ways kids in United States can practice GCF of 12 and 32 with numbers?
8.What role do numbers and GCF of 12 and 32 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve GCF of 12 and 32 skills?
Important Glossaries for GCF of 12 and 32
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
- 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 12 are 2 and 3.
- Common Factor: A number that is a factor of two or more numbers. For example, the common factors of 12 and 32 are 1, 2, and 4.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 12 and 32 is 4, as it is their largest common factor that divides the numbers completely.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 32 is divided by 12, the remainder is 8 and the quotient is 2.
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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.
