Last updated on August 5th, 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.
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.
To find the GCF of 16 and 81, a few methods are described below:
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
If the GCF of 16 and ‘b’ is 1, and the LCM is 1296. Find ‘b’.
The value of ‘b’ is 81.
GCF x LCM = product of the numbers
1 × 1296 = 16 × b
1296 = 16b
b = 1296 ÷ 16 = 81
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.
: She loves to read number jokes and games.