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109 LearnersLast updated on August 14, 2025
GCF of 3 and 20
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 3 and 20.
What is the GCF of 3 and 20?
The greatest common factor of 3 and 20 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 3 and 20?
To find the GCF of 3 and 20, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 3 and 20 by Using Listing of Factors
Steps to find the GCF of 3 and 20 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 3 = 1, 3. Factors of 20 = 1, 2, 4, 5, 10, 20.
Step 2: Now, identify the common factors of them Common factors of 3 and 20: 1.
Step 3: Choose the largest factor The largest factor that both numbers have is 1. The GCF of 3 and 20 is 1.
GCF of 3 and 20 Using Prime Factorization
To find the GCF of 3 and 20 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 3: 3 = 3 Prime Factors of 20: 20 = 2 x 2 x 5 = 2² x 5
Step 2: Now, identify the common prime factors The common prime factor is: 1 (since there are no common prime factors other than 1)
Step 3: Multiply the common prime factors The Greatest Common Factor of 3 and 20 is 1.
GCF of 3 and 20 Using Division Method or Euclidean Algorithm Method
Find the GCF of 3 and 20 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 20 by 3 20 ÷ 3 = 6 (quotient), The remainder is calculated as 20 − (3×6) = 2 The remainder is 2, not zero, so continue the process
Step 2: Now divide the previous divisor (3) by the previous remainder (2) Divide 3 by 2 3 ÷ 2 = 1 (quotient), remainder = 3 − (2×1) = 1 The remainder is 1, not zero, so continue the process
Step 3: Now divide the previous divisor (2) by the previous remainder (1) 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 3 and 20 is 1.
Common Mistakes and How to Avoid Them in GCF of 3 and 20
Finding GCF of 3 and 20 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 3, 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 a non-existent 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. 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 greater than 1
Students may assume that the GCF of two numbers will always be greater than 1. But it's not true that a GCF can also be 1. To avoid this, students should focus on common factors rather than assumptions.
Greatest Common Factor of 3 and 20 Examples
Problem 1
A teacher has 3 apples and 20 bananas. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?
We should find GCF of 3 and 20 GCF of 3 and 20 is 1.
There are 1 equal groups 3 ÷ 1 = 3 20 ÷ 1 = 20
There will be 1 group, and each group gets 3 apples and 20 bananas.
Explanation
As the GCF of 3 and 20 is 1, the teacher can make only 1 group. Now divide 3 and 20 by 1. Each group gets 3 apples and 20 bananas.
Problem 2
A school has 3 red chairs and 20 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?
GCF of 3 and 20 is 1. So each row will have 1 chair.
Explanation
There are 3 red and 20 blue chairs. To find the total number of chairs in each row, we should find the GCF of 3 and 20. There will be 1 chair in each row.
Problem 3
A tailor has 3 meters of red ribbon and 20 meters of blue ribbon. She wants to cut both ribbons into pieces of equal length, using the longest possible length. What should be the length of each piece?
For calculating longest equal length, we have to calculate the GCF of 3 and 20 The GCF of 3 and 20 is 1. The ribbon is 1 meter long.
Explanation
For calculating the longest length of the ribbon first we need to calculate the GCF of 3 and 20 which is 1. The length of each piece of the ribbon will be 1 meter.
Problem 4
A carpenter has two wooden planks, one 3 cm long and the other 20 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 3 and 20 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, 3 cm and 20 cm, respectively. We have to find the GCF of 3 and 20, which is 1 cm. The longest length of each piece is 1 cm.
Problem 5
If the GCF of 3 and ‘a’ is 1, and the LCM is 60. Find ‘a’.
The value of ‘a’ is 20.
Explanation
GCF x LCM = product of the numbers
1 × 60 = 3 × a
60 = 3a
a = 60 ÷ 3 = 20
FAQs on the Greatest Common Factor of 3 and 20
1.What is the LCM of 3 and 20?
2.Is 3 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 20?
5.Are 3 and 20 prime numbers?
Important Glossaries for GCF of 3 and 20
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 10 are 1, 2, 5, and 10.
- Prime Numbers: Numbers that have only two factors, 1 and the number itself. For example, 3 is a prime number.
- Common Factor: A number that is a factor of two or more numbers. The common factor of 3 and 20 is 1.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 3 and 20 is 1.
- LCM: The smallest common multiple of two or more numbers. For example, the LCM of 3 and 20 is 60.
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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.
