104 LearnersLast updated on August 5th, 2025
GCF of 5 and 13
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 5 and 13.
What is the GCF of 5 and 13?
The greatest common factor of 5 and 13 is 1. 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 13?
To find the GCF of 5 and 13, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 5 and 13 by Using Listing of Factors
Steps to find the GCF of 5 and 13 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 5 = 1, 5.
Factors of 13 = 1, 13.
Step 2: Now, identify the common factors of them Common factor of 5 and 13: 1.
Step 3: Choose the largest factor The largest factor that both numbers have is 1.
The GCF of 5 and 13 is 1.
GCF of 5 and 13 Using Prime Factorization
To find the GCF of 5 and 13 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 13: 13 = 13
Step 2: Now, identify the common prime factors There are no common prime factors.
Step 3: The GCF is the product of the common prime factors, which is 1.
The Greatest Common Factor of 5 and 13 is 1.
GCF of 5 and 13 Using Division Method or Euclidean Algorithm Method
Find the GCF of 5 and 13 using the division method or Euclidean Algorithm Method.
Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 13 by 5 13 ÷ 5 = 2 (quotient), The remainder is calculated as 13 − (5×2) = 3
The remainder is 3, not zero, so continue the process
Step 2: Now divide the previous divisor (5) by the previous remainder (3) Divide 5 by 3 5 ÷ 3 = 1 (quotient), remainder = 5 − (3×1) = 2
Continue the process: Divide 3 by 2 3 ÷ 2 = 1 (quotient), remainder = 3 − (2×1) = 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 5 and 13 is 1.
Common Mistakes and How to Avoid Them in GCF of 5 and 13
Finding the GCF of 5 and 13 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 indicates an 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 Greater Than 1
Students may assume that the GCF of two numbers is always greater than 1. But it's not true; GCF can also be 1, especially when dealing with co-prime numbers.
To avoid this, students should focus on common factors rather than assumptions.
Greatest Common Factor of 5 and 13 Examples
Problem 1
A gardener has 5 apple trees and 13 orange trees. She wants to plant them in rows, with each row having the same number of trees. What is the largest number of trees that can be in each row?
We should find the GCF of 5 and 13.
The GCF of 5 and 13 is 1.
There will be 1 tree per row.
Explanation
As the GCF of 5 and 13 is 1, the gardener can only plant 1 tree in each row.
Problem 2
A cook has 5 kilos of rice and 13 kilos of beans. She wants to pack them into bags with the same weight for each bag. What should be the weight of each bag?
The GCF of 5 and 13 is 1.
Each bag will have 1 kilo of either rice or beans.
Explanation
Since the GCF of 5 and 13 is 1, each bag can be packed with 1 kilo, either of rice or beans.
Problem 3
A painter has 5 brushes and 13 cans of paint. He wants to distribute them equally among several painters. What is the largest number of painters that can receive an equal share?
For equal distribution, we find the GCF of 5 and 13.
The GCF of 5 and 13 is 1.
Each painter can receive 1 brush or 1 can of paint.
Explanation
To distribute equally, the GCF of 5 and 13 is 1, so each painter can receive 1 item.
Problem 4
A farmer has two fields, one with 5 acres and the other with 13 acres. He wants to divide them into the largest possible equal plots. What should be the size of each plot?
The farmer needs the largest plot size.
The GCF of 5 and 13 is 1.
Each plot will be 1 acre.
Explanation
To find the largest plot size, the GCF of 5 and 13 is 1. Each plot will be 1 acre.
Problem 5
If the GCF of 5 and 'b' is 1, and the LCM is 65, find 'b'.
The value of 'b' is 13.
Explanation
GCF x LCM =
product of the numbers 1 × 65 =
5 × b 65 = 5b
b = 65 ÷ 5 = 13
FAQs on the Greatest Common Factor of 5 and 13
1.What is the LCM of 5 and 13?
2.Is 5 a prime number?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 13?
5.Are 5 and 13 co-prime numbers?
6.How can children in United States use numbers in everyday life to understand GCF of 5 and 13?
7.What are some fun ways kids in United States can practice GCF of 5 and 13 with numbers?
8.What role do numbers and GCF of 5 and 13 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 5 and 13 skills?
Important Glossaries for GCF of 5 and 13
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 5 are 1 and 5.
- Prime Numbers: These are numbers greater than 1 that have no divisors other than 1 and themselves. For example, 5 and 13 are prime numbers.
- Co-prime Numbers: Two numbers are co-prime if their GCF is 1. For example, 5 and 13 are co-prime.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 13 is divided by 5, the remainder is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 5 and 13 is 65.
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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.
