102 LearnersLast updated on August 5th, 2025
GCF of 80 and 125
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 80 and 125.
What is the GCF of 80 and 125?
The greatest common factor of 80 and 125 is 5. 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 80 and 125?
To find the GCF of 80 and 125, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 80 and 125 by Using Listing of Factors
Steps to find the GCF of 80 and 125 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80.
Factors of 125 = 1, 5, 25, 125.
Step 2: Now, identify the common factors of them Common factors of 80 and 125: 1, 5.
Step 3: Choose the largest factor
The largest factor that both numbers have is 5.
The GCF of 80 and 125 is 5.
GCF of 80 and 125 Using Prime Factorization
To find the GCF of 80 and 125 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 80: 80 = 2 x 2 x 2 x 2 x 5 = 2^4 x 5
Prime Factors of 125: 125 = 5 x 5 x 5 = 5^3
Step 2: Now, identify the common prime factors
The common prime factor is: 5
Step 3: Multiply the common prime factors 5 = 5.
The Greatest Common Factor of 80 and 125 is 5.
GCF of 80 and 125 Using Division Method or Euclidean Algorithm Method
Find the GCF of 80 and 125 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 125 by 80 125 ÷ 80 = 1 (quotient),
The remainder is calculated as 125 − (80 x 1) = 45
The remainder is 45, not zero, so continue the process
Step 2: Now divide the previous divisor (80) by the previous remainder (45)
Divide 80 by 45 80 ÷ 45 = 1 (quotient), remainder = 80 − (45 x 1) = 35
Continue the process
Step 3: Now divide the previous divisor (45) by the previous remainder (35)
Divide 45 by 35 45 ÷ 35 = 1 (quotient), remainder = 45 − (35 x 1) = 10
Continue the process
Step 4: Now divide the previous divisor (35) by the previous remainder (10)
Divide 35 by 10 35 ÷ 10 = 3 (quotient), remainder = 35 − (10 x 3) = 5
Continue the process
Step 5: Now divide the previous divisor (10) by the previous remainder (5)
Divide 10 by 5 10 ÷ 5 = 2 (quotient), remainder = 10 − (5 x 2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 80 and 125 is 5.
Common Mistakes and How to Avoid Them in GCF of 80 and 125
Finding the GCF of 80 and 125 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 80, students may mention 45, 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 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 an Even Number
Students may assume that the GCF of two numbers will always be an even number. But it's not true; 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 80 and 125 Examples
Problem 1
A chef has 80 apples and 125 bananas. She wants to create fruit baskets with the largest number of items in each basket. How many items will be in each basket?
We should find the GCF of 80 and 125 GCF of 80 and 125 = 5.
There are 5 equal groups 80 ÷ 5 = 16
125 ÷ 5 = 25
There will be 5 baskets, and each basket gets 16 apples and 25 bananas.
Explanation
As the GCF of 80 and 125 is 5, the chef can make 5 baskets. Now divide 80 and 125 by 5. Each basket gets 16 apples and 25 bananas.
Problem 2
A school has 80 red balls and 125 blue balls. They want to arrange them in rows with the same number of balls in each row, using the largest possible number of balls per row. How many balls will be in each row?
GCF of 80 and 125 = 5.
So each row will have 5 balls.
Explanation
There are 80 red and 125 blue balls. To find the total number of balls in each row, we should find the GCF of 80 and 125. There will be 5 balls in each row.
Problem 3
A tailor has 80 meters of red fabric and 125 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 80 and 125
The GCF of 80 and 125 = 5
Each piece of fabric will be 5 meters long.
Explanation
For calculating the longest length of the fabric first we need to calculate the GCF of 80 and 125, which is 5. The length of each piece of the fabric will be 5 meters.
Problem 4
A carpenter has two wooden planks, one 80 cm long and the other 125 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 80 and 125 = 5.
The longest length of each piece is 5 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 80 cm and 125 cm, respectively. We have to find the GCF of 80 and 125, which is 5 cm. The longest length of each piece is 5 cm.
Problem 5
If the GCF of 80 and ‘b’ is 5, and the LCM is 2000. Find ‘b’.
The value of ‘b’ is 125.
Explanation
GCF x LCM = product of the numbers 5 × 2000 = 80 × b
10000 = 80b
b = 10000 ÷ 80 = 125
FAQs on the Greatest Common Factor of 80 and 125
1.What is the LCM of 80 and 125?
2.Is 80 divisible by 8?
3.What will be the GCF of any two co-prime numbers?
4.What is the prime factorization of 125?
5.Are 80 and 125 prime numbers?
6.How can children in United States use numbers in everyday life to understand GCF of 80 and 125?
7.What are some fun ways kids in United States can practice GCF of 80 and 125 with numbers?
8.What role do numbers and GCF of 80 and 125 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve GCF of 80 and 125 skills?
Important Glossaries for GCF of 80 and 125
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 10 are 1, 2, 5, and 10.
- 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 15 is divided by 4, the remainder is 3, and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 80 and 125 is 2000.
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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.
