Summarize this article:
101 LearnersLast updated on September 9, 2025
GCF of 64 and 80
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, group or arrange items, and schedule events. In this topic, we will learn about the GCF of 64 and 80.
What is the GCF of 64 and 80?
The greatest common factor of 64 and 80 is 16. 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 64 and 80?
To find the GCF of 64 and 80, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 64 and 80 by Using Listing of Factors
Steps to find the GCF of 64 and 80 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 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80.
Step 2: Now, identify the common factors of them Common factors of 64 and 80: 1, 2, 4, 8, 16.
Step 3: Choose the largest factor The largest factor that both numbers have is 16. The GCF of 64 and 80 is 16.
GCF of 64 and 80 Using Prime Factorization
To find the GCF of 64 and 80 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 = 26
Prime Factors of 80: 80 = 2 x 2 x 2 x 2 x 5 = 24 x 5
Step 2: Now, identify the common prime factors The common prime factors are: 2 x 2 x 2 x 2 = 24
Step 3: Multiply the common prime factors 24 = 16. The Greatest Common Factor of 64 and 80 is 16.
GCF of 64 and 80 Using Division Method or Euclidean Algorithm Method
Find the GCF of 64 and 80 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 80 by 64 80 ÷ 64 = 1 (quotient), The remainder is calculated as 80 − (64 x 1) = 16 The remainder is 16, not zero, so continue the process
Step 2: Now divide the previous divisor (64) by the previous remainder (16) Divide 64 by 16 64 ÷ 16 = 4 (quotient), remainder = 64 − (16 x 4) = 0 The remainder is zero, the divisor will become the GCF. The GCF of 64 and 80 is 16.
Common Mistakes and How to Avoid Them in GCF of 64 and 80
Finding the GCF of 64 and 80 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 64, students may mention 30 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 smallest common factor instead of the largest one.
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 indicates an incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples Instead of Factors
Students confuse factors with 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 an Even Number
Students may assume that the GCF of two numbers will always be an even number. But it's not true that a GCF can also be an odd number.
To avoid this, students should focus on common factors rather than focusing on even and odd numbers.
Greatest Common Factor of 64 and 80 Examples
Problem 1
A farmer has 64 apple trees and 80 orange trees. He wants to plant them in rows with the same number of trees of each type. How many trees will be in each row?
We should find the GCF of 64 and 80 GCF of 64 and 80 2^4 = 16. There are 16 equal groups 64 ÷ 16 = 4 80 ÷ 16 = 5 There will be 16 rows, and each row will have 4 apple trees and 5 orange trees.
Explanation
As the GCF of 64 and 80 is 16, the farmer can make 16 rows.
Now divide 64 and 80 by 16.
Each row will have 4 apple trees and 5 orange trees.
Problem 2
A library has 64 fiction books and 80 non-fiction books. They want to arrange them on shelves with the same number of books on each shelf. How many books will be on each shelf?
GCF of 64 and 80 2^4 = 16. So each shelf will have 16 books.
Explanation
There are 64 fiction and 80 non-fiction books.
To find the total number of books on each shelf, we should find the GCF of 64 and 80.
There will be 16 books on each shelf.
Problem 3
A tailor has 64 meters of red fabric and 80 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 64 and 80 The GCF of 64 and 80 2^4 = 16. The fabric is 16 meters long.
Explanation
For calculating the longest length of the fabric first we need to calculate the GCF of 64 and 80, which is 16.
The length of each piece of the fabric will be 16 meters.
Problem 4
A carpenter has two wooden planks, one 64 cm long and the other 80 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 80 2^4 = 16. The longest length of each piece is 16 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 64 cm and 80 cm, respectively.
We have to find the GCF of 64 and 80, which is 16 cm.
The longest length of each piece is 16 cm.
Problem 5
If the GCF of 64 and ‘b’ is 16, and the LCM is 320. Find ‘b’.
The value of ‘b’ is 80.
Explanation
GCF x LCM = product of the numbers
16 × 320
= 64 × b
5120 = 64b
b = 5120 ÷ 64 = 80
FAQs on the Greatest Common Factor of 64 and 80
1.What is the LCM of 64 and 80?
2.Is 64 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 80?
5.Are 64 and 80 prime numbers?
6.How can families in United States create number-rich environments to improve GCF of 64 and 80 skills?
7.What are some fun ways kids in United States can practice GCF of 64 and 80 with numbers?
8.What role do numbers and GCF of 64 and 80 play in helping children in United States develop problem-solving skills?
9.How can children in United States use numbers in everyday life to understand GCF of 64 and 80?
Important Glossaries for GCF of 64 and 80
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 16 are 1, 2, 4, 8, and 16.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 4 are 4, 8, 12, 16, 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 80 are 2 and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 80 is divided by 64, the remainder is 16 and the quotient is 1.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 64 and 80 is 320.
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.
