Summarize this article:
103 LearnersLast updated on September 24, 2025
GCF of 8 and 125
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 8 and 125.
What is the GCF of 8 and 125?
The greatest common factor of 8 and 125 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.
How to find the GCF of 8 and 125?
To find the GCF of 8 and 125, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 8 and 125 by Using Listing of factors
Steps to find the GCF of 8 and 125 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 8 = 1, 2, 4, 8.
Factors of 125 = 1, 5, 25, 125.
Step 2: Now, identify the common factors of them Common factor of 8 and 125: 1.
Step 3: Choose the largest factor The largest factor that both numbers have is 1.
The GCF of 8 and 125 is 1.
GCF of 8 and 125 Using Prime Factorization
To find the GCF of 8 and 125 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 8: 8 = 2 × 2 × 2 = 2³
Prime Factors of 125: 125 = 5 × 5 × 5 = 5³
Step 2: Now, identify the common prime factors There are no common prime factors.
Step 3: Since there are no common prime factors, the GCF is 1.
The Greatest Common Factor of 8 and 125 is 1.
GCF of 8 and 125 Using Division Method or Euclidean Algorithm Method
Find the GCF of 8 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 8 125 ÷ 8 = 15 (quotient),
The remainder is calculated as 125 − (8×15) = 5
The remainder is 5, not zero, so continue the process
Step 2: Now divide the previous divisor (8) by the previous remainder (5)
Divide 8 by 5 8 ÷ 5 = 1 (quotient), remainder = 8 − (5×1) = 3
Step 3: Now divide the previous divisor (5) by the previous remainder (3)
Divide 5 by 3 5 ÷ 3 = 1 (quotient), remainder = 5 − (3×1) = 2
Step 4: Now divide the previous divisor (3) by the previous remainder (2)
Divide 3 by 2 3 ÷ 2 = 1 (quotient), remainder = 3 − (2×1) = 1
Step 5: Now divide the previous divisor (2) by the previous remainder (1)
Divide 2 by 1 2 ÷ 1 = 2 (quotient), remainder = 2 − (1×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 8 and 125 is 1.
Common Mistakes and How to Avoid Them in GCF of 8 and 125
Finding the GCF of 8 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 8, 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 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 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; the GCF can be 1 if the numbers are co-prime. To avoid this, students should focus on common factors.
Greatest Common Factor of 8 and 125 Examples
Problem 1
A teacher has 8 apples and 125 oranges. She wants to create packages containing equal numbers of apples and oranges, with the largest number of each fruit in each package. How many fruits will be in each package?
We should find the GCF of 8 and 125.
The GCF of 8 and 125 is 1.
Each package will contain 1 apple and 1 orange.
Explanation
As the GCF of 8 and 125 is 1, the teacher can only make packages containing 1 apple and 1 orange.
Problem 2
A school is organizing a competition and has 8 red flags and 125 blue flags. They want to arrange them in rows with the same number of flags in each row, using the largest possible number of flags per row. How many flags will be in each row?
The GCF of 8 and 125 is 1.
So each row will have 1 flag of each color.
Explanation
There are 8 red and 125 blue flags.
To find the total number of flags in each row, we should find the GCF of 8 and 125.
There will be 1 flag of each color in each row.
Problem 3
A tailor has 8 meters of red ribbon and 125 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 8 and 125.
The GCF of 8 and 125 is 1.
Each piece of ribbon will be 1 meter long.
Explanation
For calculating the longest length of the ribbon, first we need to calculate the GCF of 8 and 125, which is 1.
The length of each piece of the ribbon will be 1 meter.
Problem 4
A carpenter has two wooden planks, one 8 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.
The GCF of 8 and 125 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, 8 cm and 125 cm respectively, we have to find the GCF of 8 and 125, which is 1 cm.
The longest length of each piece is 1 cm.
Problem 5
If the GCF of 8 and ‘a’ is 1, and the LCM is 1000, find ‘a’.
The value of ‘a’ is 125.
Explanation
GCF × LCM = product of the numbers
1 × 1000 = 8 × a
1000 = 8a
a = 1000 ÷ 8 = 125
FAQs on the Greatest Common Factor of 8 and 125
1.What is the LCM of 8 and 125?
2.Is 8 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 125?
5.Are 8 and 125 prime numbers?
Important Glossaries for GCF of 8 and 125
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 8 are 1, 2, 4, and 8.
- 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 8 are 2 × 2 × 2.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 8 is divided by 5, the remainder is 3 and the quotient is 1.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 8 and 125 is 1000.
Explore More numbers
![Important Math Links Icon]()
Previous to GCF of 8 and 125
![Important Math Links Icon]()
Next to GCF of 8 and 125
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.
