Summarize this article:
106 LearnersLast updated on September 19, 2025
GCF of 3 and 75
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 schedule events. In this topic, we will learn about the GCF of 3 and 75.
What is the GCF of 3 and 75?
The greatest common factor of 3 and 75 is 3. 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 3 and 75?
To find the GCF of 3 and 75, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 3 and 75 by Using Listing of Factors
Steps to find the GCF of 3 and 75 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 3 = 1, 3.
Factors of 75 = 1, 3, 5, 15, 25, 75.
Step 2: Now, identify the common factors of them Common factors of 3 and 75: 1, 3.
Step 3: Choose the largest factor The largest factor that both numbers have is 3.
The GCF of 3 and 75 is 3.
GCF of 3 and 75 Using Prime Factorization
To find the GCF of 3 and 75 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 3: 3 = 3
Prime Factors of 75: 75 = 3 × 5 × 5 = 3 × 5²
Step 2: Now, identify the common prime factors
The common prime factor is: 3
Step 3: Multiply the common prime factors The Greatest Common Factor of 3 and 75 is 3.
GCF of 3 and 75 Using Division Method or Euclidean Algorithm Method
Find the GCF of 3 and 75 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 75 by 3 75 ÷ 3 = 25 (quotient),
The remainder is calculated as 75 − (3×25) = 0
The remainder is zero, so the divisor will become the GCF.
The GCF of 3 and 75 is 3.
Common Mistakes and How to Avoid Them in GCF of 3 and 75
Finding GCF of 3 and 75 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 75, students may mention 10, 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 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 3 and 75 Examples
Problem 1
A gardener has 3 large pots and 75 small pots. She wants to organize them into groups with the largest number of pots in each group. How many pots will be in each group?
We should find the GCF of 3 and 75 GCF of 3 and 75 is 3.
There are 3 equal groups 3 ÷ 3 = 1 75 ÷ 3 = 25
There will be 3 groups, and each group gets 1 large pot and 25 small pots.
Explanation
As the GCF of 3 and 75 is 3, the gardener can make 3 groups.
Now divide 3 and 75 by 3.
Each group gets 1 large pot and 25 small pots.
Problem 2
A club has 3 footballs and 75 cones. They want to arrange them in sets with the same number of items in each set, using the largest possible number of items per set. How many items will be in each set?
GCF of 3 and 75 is 3.
So each set will have 3 items.
Explanation
There are 3 footballs and 75 cones.
To find the total number of items in each set, we should find the GCF of 3 and 75.
There will be 3 items in each set.
Problem 3
A chef has 3 liters of milk and 75 liters of juice. He wants to pour them into containers of equal capacity, using the largest possible capacity for each container. What should be the capacity of each container?
For calculating the longest equal capacity, we have to calculate the GCF of 3 and 75
The GCF of 3 and 75 is 3.
The capacity of each container is 3 liters.
Explanation
For calculating the longest capacity of each container, first, we need to calculate the GCF of 3 and 75, which is 3.
The capacity of each container will be 3 liters.
Problem 4
A painter has two canvases, one 3 cm wide and the other 75 cm wide. He wants to cut them into the widest possible equal strips, without any canvas left over. What should be the width of each strip?
The painter needs the widest strip of canvas GCF of 3 and 75 is 3.
The widest width of each strip is 3 cm.
Explanation
To find the widest width of each strip of the two canvases, 3 cm and 75 cm, respectively, we have to find the GCF of 3 and 75, which is 3 cm.
The widest width of each strip is 3 cm.
Problem 5
If the GCF of 3 and ‘b’ is 3, and the LCM is 225, find ‘b’.
The value of ‘b’ is 75.
Explanation
GCF x LCM = product of the numbers
3 × 225 = 3 × b
675 = 3b
b = 675 ÷ 3 = 225
FAQs on the Greatest Common Factor of 3 and 75
1.What is the LCM of 3 and 75?
2.Is 75 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 75?
5.Are 3 and 75 prime numbers?
Important Glossaries for GCF of 3 and 75
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 3 are 1 and 3.
- 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 75 are 3 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.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 3 and 75 is 75.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 3 and 75 will be 3, as it is their largest common factor that divides the numbers completely.
Explore More numbers
![Important Math Links Icon]()
Previous to GCF of 3 and 75
![Important Math Links Icon]()
Next to GCF of 3 and 75
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.
