GCF of 16 and 81
2026-02-28 23:39 Diff
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Last updated on August 5, 2025

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.

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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.

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?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

Problem 5

If the GCF of 16 and ‘b’ is 1, and the LCM is 1296. Find ‘b’.

Okay, lets begin

The value of ‘b’ is 81.

Explanation

GCF x LCM = product of the numbers

1 × 1296 = 16 × b

1296 = 16b

b = 1296 ÷ 16 = 81

Well explained 👍

FAQs on the Greatest Common Factor of 16 and 81

1.What is the LCM of 16 and 81?

The LCM of 16 and 81 is 1296.

2.Is 16 divisible by 4?

Yes, 16 is divisible by 4 because 16 ÷ 4 = 4.

3.What will be the GCF of any two consecutive numbers?

4.What is the prime factorization of 81?

The prime factorization of 81 is 34.

5.Are 16 and 81 prime numbers?

No, 16 and 81 are not prime numbers because both of them have more than two factors.

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.