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118 LearnersLast updated on August 11, 2025
GCF of 5 and 20
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 5 and 20.
What is the GCF of 5 and 20?
The greatest common factor of 5 and 20 is 5. 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 5 and 20?
To find the GCF of 5 and 20, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 5 and 20 by Using Listing of Factors
Steps to find the GCF of 5 and 20 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 5 = 1, 5. Factors of 20 = 1, 2, 4, 5, 10, 20.
Step 2: Now, identify the common factors of them Common factors of 5 and 20: 1, 5.
Step 3: Choose the largest factor The largest factor that both numbers have is 5.
The GCF of 5 and 20 is 5.
GCF of 5 and 20 Using Prime Factorization
To find the GCF of 5 and 20 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 5: 5 = 5 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: 5
Step 3: Multiply the common prime factors 5
The Greatest Common Factor of 5 and 20 is 5.
GCF of 5 and 20 Using Division Method or Euclidean Algorithm Method
Find the GCF of 5 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 5 20 ÷ 5 = 4 (quotient), The remainder is calculated as 20 − (5×4) = 0 The remainder is zero, so the divisor will become the GCF.
The GCF of 5 and 20 is 5.
Common Mistakes and How to Avoid Them in GCF of 5 and 20
Finding the GCF of 5 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 5, 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 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 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 5 and 20 Examples
Problem 1
A gardener has 5 roses and 20 tulips. She wants to create bouquets with the largest possible number of flowers in each. How many flowers will be in each bouquet?
We should find the GCF of 5 and 20. GCF of 5 and 20 is 5.
There are 5 flowers in each bouquet. 5 ÷ 5 = 1 20 ÷ 5 = 4
There will be 5 bouquets, and each bouquet gets 1 rose and 4 tulips.
Explanation
As the GCF of 5 and 20 is 5, the gardener can make 5 bouquets.
Now divide 5 and 20 by 5.
Each bouquet gets 1 rose and 4 tulips.
Problem 2
A library has 5 mystery novels and 20 science fiction novels. They want to arrange them in shelves with the same number of books on each shelf, using the largest possible number of books per shelf. How many books will be on each shelf?
GCF of 5 and 20 is 5. So each shelf will have 5 books.
Explanation
There are 5 mystery novels and 20 science fiction novels.
To find the total number of books on each shelf, we should find the GCF of 5 and 20.
There will be 5 books on each shelf.
Problem 3
A chef has 5 kilograms of apples and 20 kilograms of bananas. He wants to divide them into bags of equal weight, using the heaviest possible weight. What should be the weight of each bag?
For calculating the heaviest equal weight, we have to calculate the GCF of 5 and 20.
The GCF of 5 and 20 is 5.
Each bag will weigh 5 kilograms.
Explanation
For calculating the heaviest weight of the bags, first, we need to calculate the GCF of 5 and 20, which is 5.
The weight of each bag will be 5 kilograms.
Problem 4
A technician has two cables, one 5 meters long and the other 20 meters long. He wants to cut them into the longest possible equal pieces, without any cable left over. What should be the length of each piece?
The technician needs the longest piece of cable. GCF of 5 and 20 is 5.
The longest length of each piece is 5 meters.
Explanation
To find the longest length of each piece of the two cables, 5 meters and 20 meters, respectively, we have to find the GCF of 5 and 20, which is 5 meters.
The longest length of each piece is 5 meters.
Problem 5
If the GCF of 5 and ‘b’ is 5, and the LCM is 20, find ‘b’.
The value of ‘b’ is 20.
Explanation
GCF x LCM = product of the numbers 5 × 20 = 5 × b 100 = 5b b = 100 ÷ 5 = 20
FAQs on the Greatest Common Factor of 5 and 20
1.What is the LCM of 5 and 20?
2.Is 5 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 20?
5.Are 5 and 20 prime numbers?
Important Glossaries for GCF of 5 and 20
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 20 are 1, 2, 4, 5, 10, and 20.
- 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 20 are 2 and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 20 is divided by 6, the remainder is 2, and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 5 and 20 is 20.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 5 and 20 is 5, as it is their largest common factor that divides the numbers completely.
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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.
