101 LearnersLast updated on August 5th, 2025
GCF of 20 and 32
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 to schedule events. In this topic, we will learn about the GCF of 20 and 32.
What is the GCF of 20 and 32?
The greatest common factor of 20 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 20 and 32?
To find the GCF of 20 and 32, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 20 and 32 by Using Listing of Factors
Steps to find the GCF of 20 and 32 using the listing of factors:
Step 1: Firstly, list the factors of each number:
Factors of 20 = 1, 2, 4, 5, 10, 20.
Factors of 32 = 1, 2, 4, 8, 16, 32.
Step 2: Now, identify the common factors of them Common factors of 20 and 32: 1, 2, 4.
Step 3: Choose the largest factor:
The largest factor that both numbers have is 4.
The GCF of 20 and 32 is 4.
GCF of 20 and 32 Using Prime Factorization
To find the GCF of 20 and 32 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime factors of 20: 20 = 2 x 2 x 5 = 22 x 5
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 20 and 32 is 4.
GCF of 20 and 32 Using Division Method or Euclidean Algorithm Method
Find the GCF of 20 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 20 32 ÷ 20 = 1 (quotient), The remainder is calculated as 32 − (20×1) = 12
The remainder is 12, not zero, so continue the process
Step 2: Now divide the previous divisor (20) by the previous remainder (12)
Divide 20 by 12 20 ÷ 12 = 1 (quotient), remainder = 20 − (12×1) = 8 Now, divide 12 by 8 12 ÷ 8 = 1 (quotient), remainder = 12 − (8×1) = 4
Now, divide 8 by 4 8 ÷ 4 = 2 (quotient), remainder = 8 − (4×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 20 and 32 is 4.
Common Mistakes and How to Avoid Them in GCF of 20 and 32
Finding GCF of 20 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 20, 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 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 20 and 32 Examples
Problem 1
A gardener has 20 rose bushes and 32 tulip bulbs. She wants to plant them in equal rows with the largest number of plants in each row. How many plants will be in each row?
We should find the GCF of 20 and 32 The GCF of 20 and 32
22 = 4.
There are 4 equal rows
20 ÷ 4 = 5
32 ÷ 4 = 8
There will be 4 rows, and each row has 5 rose bushes and 8 tulip bulbs.
Explanation
As the GCF of 20 and 32 is 4, the gardener can make 4 rows.
Now divide 20 and 32 by 4.
Each row gets 5 rose bushes and 8 tulip bulbs.
Problem 2
A school has 20 red balls and 32 blue balls. They want to arrange them in groups with the same number of balls in each group, using the largest possible number of balls per group. How many balls will be in each group?
The GCF of 20 and 32
22 = 4.
So each group will have 4 balls.
Explanation
There are 20 red and 32 blue balls. To find the total number of balls in each group, we should find the GCF of 20 and 32. There will be 4 balls in each group.
Problem 3
A chef has 20 kilograms of flour and 32 kilograms of sugar. He wants to divide both into equal portions of the longest possible length. What should be the weight of each portion?
For calculating the longest equal portion weight, we have to calculate the GCF of 20 and 32
The GCF of 20 and 32
22 = 4.
Each portion is 4 kilograms.
Explanation
For calculating the longest portion weight, first, we need to calculate the GCF of 20 and 32, which is 4. The weight of each portion will be 4 kilograms.
Problem 4
A carpenter has two wooden planks, one 20 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
The GCF of 20 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, 20 cm and 32 cm, respectively, we have to find the GCF of 20 and 32, which is 4 cm.
The longest length of each piece is 4 cm.
Problem 5
If the GCF of 20 and ‘a’ is 4, and the LCM is 160, find ‘a’.
The value of ‘a’ is 32.
Explanation
GCF x LCM = product of the numbers
4 × 160 = 20 × a
640 = 20a
a = 640 ÷ 20 = 32
FAQs on the Greatest Common Factor of 20 and 32
1.What is the LCM of 20 and 32?
2.Is 20 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 32?
5.Are 20 and 32 prime numbers?
6.How can children in United States use numbers in everyday life to understand GCF of 20 and 32?
7.What are some fun ways kids in United States can practice GCF of 20 and 32 with numbers?
8.What role do numbers and GCF of 20 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 20 and 32 skills?
Important Glossaries for GCF of 20 and 32
- 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 3 are 3, 6, 9, 12, 15, 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 and the quotient is 2.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 20 and 32 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.
