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101 LearnersLast updated on September 9, 2025
GCF of 27 and 64
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 to schedule events. In this topic, we will learn about the GCF of 27 and 64.
What is the GCF of 27 and 64?
The greatest common factor of 27 and 64 is 1. The largest divisor of two or more numbers is called the GCF of the numbers.
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 27 and 64?
To find the GCF of 27 and 64, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 27 and 64 by Using Listing of Factors
Steps to find the GCF of 27 and 64 using the listing of factors:
Step 1: Firstly, list the factors of each number Factors of 27 = 1, 3, 9, 27. Factors of 64 = 1, 2, 4, 8, 16, 32, 64.
Step 2: Now, identify the common factors of them Common factor of 27 and 64: 1.
Step 3: Choose the largest factor The largest factor that both numbers have is 1. The GCF of 27 and 64 is 1.
GCF of 27 and 64 Using Prime Factorization
To find the GCF of 27 and 64 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 27: 27 = 3 x 3 x 3 = 3³ Prime Factors of 64: 64 = 2 x 2 x 2 x 2 x 2 x 2 = 2⁶
Step 2: Now, identify the common prime factors There are no common prime factors.
Step 3: Multiply the common prime factors No common prime factors exist, so the GCF is 1. The Greatest Common Factor of 27 and 64 is 1.
GCF of 27 and 64 Using Division Method or Euclidean Algorithm Method
Find the GCF of 27 and 64 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 64 by 27 64 ÷ 27 = 2 (quotient) The remainder is calculated as 64 − (27×2) = 10 The remainder is 10, not zero, so continue the process
Step 2: Now divide the previous divisor (27) by the previous remainder (10) 27 ÷ 10 = 2 (quotient), remainder = 27 − (10×2) = 7
Step 3: Divide 10 by 7 10 ÷ 7 = 1 (quotient), remainder = 10 − (7×1) = 3
Step 4: Divide 7 by 3 7 ÷ 3 = 2 (quotient), remainder = 7 − (3×2) = 1
Step 5: Divide 3 by 1 3 ÷ 1 = 3 (quotient), remainder = 3 − (1×3) = 0 The remainder is zero, so the divisor will become the GCF. The GCF of 27 and 64 is 1.
Common Mistakes and How to Avoid Them in GCF of 27 and 64
Finding the GCF of 27 and 64 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 27, 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 largest factor of one number instead of the common factor.
To avoid this confusion, students should list all the common factors and find the greatest 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 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 the GCF of two numbers will always be greater than 1. But it's not true; a GCF can be 1 if the numbers are co-prime.
To avoid this, students should focus on common factors rather than assumptions.
Greatest Common Factor of 27 and 64 Examples
Problem 1
A farmer has 27 apple trees and 64 pear trees. She wants to plant them in rows with an equal number of trees in each row, using the largest possible number of trees per row. How many trees will be in each row?
We should find the GCF of 27 and 64 The GCF of 27 and 64 is 1. There will be 1 tree in each row.
Explanation
As the GCF of 27 and 64 is 1, the farmer can plant only 1 tree in each row.
Problem 2
A baker has 27 loaves of bread and 64 pastries. They want to package them in boxes with the same number of items in each box, using the largest possible number of items per box. How many items will be in each box?
The GCF of 27 and 64 is 1. So there will be 1 item in each box.
Explanation
There are 27 loaves and 64 pastries.
To find the total number of items in each box, we should find the GCF of 27 and 64.
There will be 1 item in each box.
Problem 3
A designer has 27 meters of red fabric and 64 meters of blue fabric. She wants to cut both fabrics 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 27 and 64 The GCF of 27 and 64 is 1. The length of each piece is 1 meter.
Explanation
For calculating the longest length of the fabric, we first need to calculate the GCF of 27 and 64, which is 1.
The length of each piece of fabric will be 1 meter.
Problem 4
A carpenter has two wooden planks, one 27 cm long and the other 64 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 The GCF of 27 and 64 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, 27 cm and 64 cm, respectively, we have to find the GCF of 27 and 64, which is 1 cm.
The longest length of each piece is 1 cm.
Problem 5
If the GCF of 27 and ‘b’ is 1, and the LCM is 1728, find ‘b’.
The value of ‘b’ is 64.
Explanation
GCF x LCM = product of the numbers
1 × 1728
= 27 × b 1728
= 27b b
= 1728 ÷ 27 = 64
FAQs on the Greatest Common Factor of 27 and 64
1.What is the LCM of 27 and 64?
2.Is 27 a perfect square?
3.What will be the GCF of any two consecutive integers?
4.What is the prime factorization of 64?
5.Are 27 and 64 prime numbers?
Important Glossaries for GCF of 27 and 64
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 9 are 1, 3, and 9.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 5 are 5, 10, 15, 20, and so on.
- 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 20 are 2 and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 3, the remainder is 1 and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 4 and 6 is 12.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 8 and 12 will be 4, as it is their largest common factor that divides the numbers completely.
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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.
