103 LearnersLast updated on August 5th, 2025
GCF of 16 and 81
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 16 and 81.
What is the GCF of 16 and 81?
The greatest common factor of 16 and 81 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 16 and 81?
To find the GCF of 16 and 81, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 16 and 81 by Using Listing of factors
Steps to find the GCF of 16 and 81 using the listing of factors:
Step 1: Firstly, list the factors of each number:
Factors of 16 = 1, 2, 4, 8, 16.
Factors of 81 = 1, 3, 9, 27, 81.
Step 2: Now, identify the common factors of them, Common factor of 16 and 81: 1.
Step 3: Choose the largest factor
The largest factor that both numbers have is 1.
The GCF of 16 and 81 is 1.
GCF of 16 and 81 Using Prime Factorization
To find the GCF of 16 and 81 using Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 16: 16 = 2 x 2 x 2 x 2 = 24
Prime Factors of 81: 81 = 3 x 3 x 3 x 3 = 34
Step 2: Now, identify the common prime factors. There are no common prime factors.
Step 3: Multiply the common prime factors Since there are no common prime factors, the GCF is 1.
The Greatest Common Factor of 16 and 81 is 1.
GCF of 16 and 81 Using Division Method or Euclidean Algorithm Method
Find the GCF of 16 and 81 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 81 by 16 81 ÷ 16 = 5 (quotient), The remainder is calculated as 81 − (16×5) = 1
The remainder is 1, not zero, so continue the process
Step 2: Now divide the previous divisor (16) by the previous remainder (1)
Divide 16 by 1 16 ÷ 1 = 16 (quotient), remainder = 16 − (1×16) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 16 and 81 is 1.
Common Mistakes and How to Avoid Them in GCF of 16 and 81
Finding GCF of 16 and 81 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 16, 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 wrong common factor instead of the correct one. To avoid this confusion, students should list all the common factors and find the correct 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 GCF of two numbers will always be greater than 1. But this is not true as the GCF can also be 1 if the numbers are co-prime. To avoid this, students should focus on common factors rather than assumptions.
Greatest Common Factor of 16 and 81 Examples
Problem 1
A chef has 16 apples and 81 oranges. She wants to create fruit baskets with all the fruits, using the largest possible equal number of fruits per basket. How many fruits will be in each basket?
We should find GCF of 16 and 81 GCF of 16 and 81 is 1.
There will be 1 fruit per basket, as 16 and 81 have no other common factors.
Explanation
As the GCF of 16 and 81 is 1, the chef can only put 1 fruit in each basket to have equal numbers of apples and oranges.
Problem 2
A gardener has 16 rose plants and 81 tulip plants. They want to plant them in rows with the same number of plants in each row, using the largest possible number of plants per row. How many plants will be in each row?
GCF of 16 and 81 is 1. So each row will have 1 plant.
Explanation
There are 16 rose plants and 81 tulip plants. To find the total number of plants in each row, we should find the GCF of 16 and 81. There will be 1 plant in each row.
Problem 3
A tailor has 16 meters of red cloth and 81 meters of blue cloth. She wants to cut both cloths into pieces of equal length, 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 16 and 81 The GCF of 16 and 81 is 1. The length of each piece is 1 meter.
Explanation
For calculating the longest length of the cloth first we need to calculate the GCF of 16 and 81 which is 1.
The length of each piece of the cloth will be 1 meter.
Problem 4
A carpenter has two wooden planks, one 16 cm long and the other 81 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 16 and 81 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, 16 cm and 81 cm, respectively.
We have to find the GCF of 16 and 81, which is 1 cm.
The longest length of each piece is 1 cm.
Problem 5
If the GCF of 16 and ‘b’ is 1, and the LCM is 1296. Find ‘b’.
The value of ‘b’ is 81.
Explanation
GCF x LCM = product of the numbers
1 × 1296 = 16 × b
1296 = 16b
b = 1296 ÷ 16 = 81
FAQs on the Greatest Common Factor of 16 and 81
1.What is the LCM of 16 and 81?
2.Is 16 divisible by 4?
3.What will be the GCF of any two consecutive numbers?
4.What is the prime factorization of 81?
5.Are 16 and 81 prime numbers?
6.How can children in United States use numbers in everyday life to understand GCF of 16 and 81?
7.What are some fun ways kids in United States can practice GCF of 16 and 81 with numbers?
8.What role do numbers and GCF of 16 and 81 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 16 and 81 skills?
Important Glossaries for GCF of 16 and 81
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 16 are 1, 2, 4, 8, and 16.
- 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 81 are 3 x 3 x 3 x 3.
- Co-prime Numbers: Two numbers that have no common factors other than 1. For example, 16 and 81 are co-prime.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 81 is divided by 16, the remainder is 1.
- LCM: The smallest common multiple of two or more numbers. For example, the LCM of 16 and 81 is 1296.
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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.
