102 LearnersLast updated on July 31st, 2025
GCF of 60 and 75
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 60 and 75.
What is the GCF of 60 and 75?
The greatest common factor of 60 and 75 is 15. 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, which are always positive.
How to find the GCF of 60 and 75?
To find the GCF of 60 and 75, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 60 and 75 by Using Listing of Factors
Steps to find the GCF of 60 and 75 using the listing of factors:
Step 1: Firstly, list the factors of each number:
Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Factors of 75 = 1, 3, 5, 15, 25, 75.
Step 2: Now, identify the common factors of them.
Common factors of 60 and 75: 1, 3, 5, 15.
Step 3: Choose the largest factor:
The largest factor that both numbers have is 15.
The GCF of 60 and 75 is 15.
GCF of 60 and 75 Using Prime Factorization
To find the GCF of 60 and 75 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number:
Prime Factors of 60: 60 = 2 x 2 x 3 x 5 = 22 x 3 x 5
Prime Factors of 75: 75 = 3 x 5 x 5 = 3 x 52
Step 2: Now, identify the common prime factors. The common prime factors are: 3 x 5
Step 3: Multiply the common prime factors 3 x 5 = 15.
The Greatest Common Factor of 60 and 75 is 15.
GCF of 60 and 75 Using Division Method or Euclidean Algorithm Method
Find the GCF of 60 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 60 75 ÷ 60 = 1 (quotient), The remainder is calculated as 75 − (60×1) = 15
The remainder is 15, not zero, so continue the process
Step 2: Now divide the previous divisor (60) by the previous remainder (15)
Divide 60 by 15 60 ÷ 15 = 4 (quotient), remainder = 60 − (15×4) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 60 and 75 is 15.
Common Mistakes and How to Avoid Them in GCF of 60 and 75
Finding GCF of 60 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 60, students may mention 50 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 between 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 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 60 and 75 Examples
Problem 1
A gardener has 60 tulips and 75 roses. He wants to plant them in rows with the same number of flowers in each row, using the largest possible number of flowers per row. How many flowers will be in each row?
We should find the GCF of 60 and 75 GCF of 60 and 75
3 x 5 = 15.
There are 15 equal rows
60 ÷ 15 = 4
75 ÷ 15 = 5
There will be 15 rows, and each row gets 4 tulips and 5 roses.
Explanation
As the GCF of 60 and 75 is 15, the gardener can make 15 rows.
Now divide 60 and 75 by 15.
Each row gets 4 tulips and 5 roses.
Problem 2
A school has 60 desks and 75 chairs. They want to arrange them in rows with the same number of items in each row, using the largest possible number of items per row. How many items will be in each row?
GCF of 60 and 75 3 x 5 = 15. So each row will have 15 items.
Explanation
There are 60 desks and 75 chairs.
To find the total number of items in each row, we should find the GCF of 60 and 75.
There will be 15 items in each row.
Problem 3
A tailor has 60 meters of green fabric and 75 meters of yellow 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 60 and 75
The GCF of 60 and 75
3 x 5 = 15.
The fabric is 15 meters long.
Explanation
For calculating the longest length of the fabric first, we need to calculate the GCF of 60 and 75, which is 15. The length of each piece of the fabric will be 15 meters.
Problem 4
A carpenter has two wooden planks, one 60 cm long and the other 75 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 60 and 75
3 x 5 = 15.
The longest length of each piece is 15 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 60 cm and 75 cm, respectively.
We have to find the GCF of 60 and 75, which is 15 cm.
The longest length of each piece is 15 cm.
Problem 5
If the GCF of 60 and ‘b’ is 15, and the LCM is 300. Find ‘b’.
The value of ‘b’ is 75.
Explanation
GCF x LCM = product of the numbers
15 × 300 = 60 × b
4500 = 60b
b = 4500 ÷ 60 = 75
FAQs on the Greatest Common Factor of 60 and 75
1.What is the LCM of 60 and 75?
2.Is 60 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 75?
5.Are 60 and 75 prime numbers?
6.How can children in United Kingdom use numbers in everyday life to understand GCF of 60 and 75?
7.What are some fun ways kids in United Kingdom can practice GCF of 60 and 75 with numbers?
8.What role do numbers and GCF of 60 and 75 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve GCF of 60 and 75 skills?
Important Glossaries for GCF of 60 and 75
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 15 are 1, 3, 5, and 15.
- 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, 25, 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 30 are 2, 3, and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 14 is divided by 4, the remainder is 2 and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 60 and 75 is 300.
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.
