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 64 and 81.
The greatest common factor of 64 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 64 and 81, a few methods are described below -
Steps to find the GCF of 64 and 81 using the listing of factors:
Step 1: Firstly, list the factors of each number.
Factors of 64 = 1, 2, 4, 8, 16, 32, 64.
Factors of 81 = 1, 3, 9, 27, 81.
Step 2: Now, identify the common factors of them.
Common factors of 64 and 81: 1.
Step 3: Choose the largest factor.
The largest factor that both numbers have is 1.
The GCF of 64 and 81 is 1.
To find the GCF of 64 and 81 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number.
Prime Factors of 64: 64 = 2 x 2 x 2 x 2 x 2 x 2 = 2^6
Prime Factors of 81: 81 = 3 x 3 x 3 x 3 = 3^4
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 64 and 81 is 1.
Find the GCF of 64 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 64. 81 ÷ 64 = 1 (quotient),
The remainder is calculated as 81 − (64×1) = 17.
The remainder is 17, not zero, so continue the process.
Step 2: Now divide the previous divisor (64) by the previous remainder (17). 64 ÷ 17 = 3 (quotient), remainder = 64 − (17×3) = 13.
Step 3: Continue the process. 17 ÷ 13 = 1 (quotient), remainder = 17 − (13×1) = 4. 13 ÷ 4 = 3 (quotient), remainder = 13 − (4×3) = 1. 4 ÷ 1 = 4 (quotient), remainder = 4 − (1×4) = 0.
The remainder is zero, the divisor will become the GCF.
The GCF of 64 and 81 is 1.
Finding the GCF of 64 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 teacher has 64 apples and 81 oranges. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?
We should find the GCF of 64 and 81.
GCF of 64 and 81 is 1.
There are 1 equal groups. 64 ÷ 1 = 64
81 ÷ 1 = 81
There will be 1 group, and each group gets 64 apples and 81 oranges.
As the GCF of 64 and 81 is 1, the teacher can make 1 group. Now divide 64 and 81 by 1. Each group gets 64 apples and 81 oranges.
A school has 64 red chairs and 81 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?
GCF of 64 and 81 is 1.
So each row will have 1 chair.
There are 64 red and 81 blue chairs. To find the total number of chairs in each row, we should find the GCF of 64 and 81. There will be 1 chair in each row.
A tailor has 64 meters of red ribbon and 81 meters of blue ribbon. She wants to cut both ribbons 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 64 and 81.
The GCF of 64 and 81 is 1.
The ribbon is 1 meter long.
For calculating the longest length of the ribbon, first, we need to calculate the GCF of 64 and 81, which is 1. The length of each piece of the ribbon will be 1 meter.
A carpenter has two wooden planks, one 64 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 64 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, 64 cm and 81 cm, respectively, we have to find the GCF of 64 and 81, which is 1 cm. The longest length of each piece is 1 cm.
If the GCF of 64 and ‘a’ is 1, and the LCM is 5184. Find ‘a’.
The value of ‘a’ is 81.
GCF x LCM = product of the numbers 1 × 5184 = 64 × a
5184 = 64a
a = 5184 ÷ 64 = 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.