101 LearnersLast updated on August 5th, 2025
GCF of 5 and 16
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 16.
What is the GCF of 5 and 16?
The greatest common factor of 5 and 16 is 1. The largest divisor of two or more numbers is called the GCF of the numbers. If two numbers are co-prime, meaning they have no common factors other than 1, 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 16?
To find the GCF of 5 and 16, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 5 and 16 by Using Listing of Factors
Steps to find the GCF of 5 and 16 using the listing of factors:
Step 1: Firstly, list the factors of each number.
Factors of 5 = 1, 5.
Factors of 16 = 1, 2, 4, 8, 16.
Step 2: Now, identify the common factors of them.
Common factor of 5 and 16: 1.
Step 3: Choose the largest factor.
The largest factor that both numbers have is 1.
The GCF of 5 and 16 is 1.
GCF of 5 and 16 Using Prime Factorization
To find the GCF of 5 and 16 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 16: 16 = 2 x 2 x 2 x 2 = 2^4
Step 2: Now, identify the common prime factors.
There are no common prime factors other than 1
Step 3: Since there's no shared prime factor, the GCF is 1.
GCF of 5 and 16 Using Division Method or Euclidean Algorithm Method
Find the GCF of 5 and 16 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number.
Here, divide 16 by 5. 16 ÷ 5 = 3 (quotient),
The remainder is calculated as 16 − (5×3) = 1.
The remainder is 1, not zero, so continue the process.
Step 2: Now divide the previous divisor (5) by the previous remainder (1).
Divide 5 by 1. 5 ÷ 1 = 5 (quotient), remainder = 5 − (1×5) = 0.
The remainder is zero, the divisor will become the GCF.
The GCF of 5 and 16 is 1.
Common Mistakes and How to Avoid Them in GCF of 5 and 16
Finding the GCF of 5 and 16 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 2, 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, which in this case is 1.
Mistake 3
Forgetting to include 1 as a factor
Sometimes students may forget 1 as a common factor of the numbers. However, it is crucial to understanding factors completely. Students should always 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 a non-trivial number
Students may assume that the GCF of two numbers will always be a number other than 1. But it's not true. The GCF can be 1 if two numbers are co-prime. To avoid this, students should focus on common factors rather than assumptions.
Greatest Common Factor of 5 and 16 Examples
Problem 1
There are 5 apples and 16 oranges. A vendor wants to pack them into baskets with the same number of fruits in each basket. How many fruits will be in each basket?
We should find the GCF of 5 and 16.
The GCF of 5 and 16 is 1.
Thus, there will be 1 fruit per basket, making a total of 21 baskets.
Explanation
As the GCF of 5 and 16 is 1, the vendor can make 21 baskets, each containing 1 fruit.
Problem 2
A gardener has 5 rose plants and 16 tulip plants. She wants to plant them in rows with the same number of plants in each row. How many plants will be in each row?
The GCF of 5 and 16 is 1.
So each row will have 1 plant.
Explanation
There are 5 rose and 16 tulip plants. To find the total number of plants in each row, we should find the GCF of 5 and 16. There will be 1 plant in each row.
Problem 3
A baker has 5 chocolate cakes and 16 vanilla cakes. She wants to cut both types of cakes into equal pieces, 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 5 and 16
The GCF of 5 and 16 is 1.
Each piece will be equivalent to 1 unit of the cake.
Explanation
For calculating the longest length of the cake pieces, first we need to calculate the GCF of 5 and 16, which is 1. The length of each piece of the cake will be 1 unit.
Problem 4
A tailor has two pieces of fabric, one 5 meters long and the other 16 meters long. He wants to cut them into the longest possible equal pieces, without any fabric left over. What should be the length of each piece?
The tailor needs the longest piece of fabric.
The GCF of 5 and 16 is 1.
The longest length of each piece is 1 meter.
Explanation
To find the longest length of each piece of the two fabrics, 5 meters and 16 meters, respectively, we have to find the GCF of 5 and 16, which is 1 meter. The longest length of each piece is 1 meter.
Problem 5
If the GCF of 5 and ‘a’ is 1, and the LCM is 80, find ‘a’.
The value of ‘a’ is 16.
Explanation
GCF x LCM = product of the numbers 1 × 80 = 5 × a
80 = 5a
a = 80 ÷ 5 = 16
FAQs on the Greatest Common Factor of 5 and 16
1.What is the LCM of 5 and 16?
2.Is 5 divisible by 2?
3.What will be the GCF of any two co-prime numbers?
4.What is the prime factorization of 16?
5.Are 5 and 16 prime numbers?
6.How can children in United States use numbers in everyday life to understand GCF of 5 and 16?
7.What are some fun ways kids in United States can practice GCF of 5 and 16 with numbers?
8.What role do numbers and GCF of 5 and 16 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 16 skills?
Important Glossaries for GCF of 5 and 16
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 5 are 1 and 5.
- Co-prime numbers: Two numbers that have no common factors other than 1. For example, 5 and 16 are co-prime.
- Prime Factors: These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factor of 5 is 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 16 is divided by 5, the remainder is 1.
- LCM: The smallest common multiple of two or more numbers is termed the LCM. For example, the LCM of 5 and 16 is 80.
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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.
