107 LearnersLast updated on August 5th, 2025
GCF of 75 and 120
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 75 and 120.
What is the GCF of 75 and 120?
The greatest common factor of 75 and 120 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 are always positive.
How to find the GCF of 75 and 120?
To find the GCF of 75 and 120, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 75 and 120 by Using Listing of Factors
Steps to find the GCF of 75 and 120 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 75 = 1, 3, 5, 15, 25, 75.
Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120.
Step 2: Now, identify the common factors of them Common factors of 75 and 120: 1, 3, 5, 15
Step 3: Choose the largest factor
The largest factor that both numbers have is 15.
The GCF of 75 and 120 is 15.
GCF of 75 and 120 Using Prime Factorization
To find the GCF of 75 and 120 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 75: 75 = 3 x 5 x 5 = 3 x 5²
Prime Factors of 120: 120 = 2 x 2 x 2 x 3 x 5 = 2³ x 3 x 5
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 75 and 120 is 15.
GCF of 75 and 120 Using Division Method or Euclidean Algorithm Method
Find the GCF of 75 and 120 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 120 by 75 120 ÷ 75 = 1 (quotient),
The remainder is calculated as 120 − (75×1) = 45
The remainder is 45, not zero, so continue the process
Step 2: Now divide the previous divisor (75) by the previous remainder (45)
Divide 75 by 45 75 ÷ 45 = 1 (quotient), remainder = 75 − (45×1) = 30
Step 3: Again, divide the previous divisor (45) by the previous remainder (30)
Divide 45 by 30 45 ÷ 30 = 1 (quotient), remainder = 45 − (30×1) = 15
Step 4: Finally, divide the previous divisor (30) by the previous remainder (15)
Divide 30 by 15 30 ÷ 15 = 2 (quotient), remainder = 30 − (15×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 75 and 120 is 15.
Common Mistakes and How to Avoid Them in GCF of 75 and 120
Finding the GCF of 75 and 120 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 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 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 75 and 120 Examples
Problem 1
A baker has 75 chocolate cupcakes and 120 vanilla cupcakes. She wants to arrange them into trays with the largest number of cupcakes in each tray. How many cupcakes will be in each tray?
We should find the GCF of 75 and 120
GCF of 75 and 120 3 x 5 = 15.
There are 15 equal trays 75 ÷ 15 = 5
120 ÷ 15 = 8
There will be 15 trays, and each tray gets 5 chocolate cupcakes and 8 vanilla cupcakes.
Explanation
As the GCF of 75 and 120 is 15, the baker can make 15 trays. Now divide 75 and 120 by 15. Each tray gets 5 chocolate cupcakes and 8 vanilla cupcakes.
Problem 2
A farmer has 75 apple trees and 120 pear trees. He wants to plant them in rows with the same number of trees in each row, using the largest possible number of trees per row. How many trees will be in each row?
GCF of 75 and 120 3 x 5 = 15.
So each row will have 15 trees.
Explanation
There are 75 apple trees and 120 pear trees. To find the total number of trees in each row, we should find the GCF of 75 and 120. There will be 15 trees in each row.
Problem 3
A tailor has 75 meters of silk fabric and 120 meters of cotton 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 75 and 120
The GCF of 75 and 120
3 x 5 = 15.
Each piece of fabric is 15 meters long.
Explanation
For calculating the longest length of the fabric, first, we need to calculate the GCF of 75 and 120, which is 15. The length of each piece of fabric will be 15 meters.
Problem 4
A carpenter has two wooden planks, one 75 cm long and the other 120 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 75 and 120
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, 75 cm and 120 cm, respectively.
We have to find the GCF of 75 and 120, which is 15 cm.
The longest length of each piece is 15 cm.
Problem 5
If the GCF of 75 and ‘b’ is 15, and the LCM is 600. Find ‘b’.
The value of ‘b’ is 120.
Explanation
GCF x LCM = product of the numbers 15 × 600 = 75 × b
9000 = 75b
b = 9000 ÷ 75 = 120
FAQs on the Greatest Common Factor of 75 and 120
1.What is the LCM of 75 and 120?
2.Is 75 divisible by 5?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 120?
5.Are 75 and 120 prime numbers?
6.How can children in India use numbers in everyday life to understand GCF of 75 and 120?
7.What are some fun ways kids in India can practice GCF of 75 and 120 with numbers?
8.What role do numbers and GCF of 75 and 120 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve GCF of 75 and 120 skills?
Important Glossaries for GCF of 75 and 120
- 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 75 are 3 and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 75 is divided by 10, the remainder is 5 and the quotient is 7.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 75 and 120 is 600.
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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.
