Last updated on August 5th, 2025
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.
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.
To find the GCF of 75 and 120, a few methods are described below -
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
If the GCF of 75 and ‘b’ is 15, and the LCM is 600. Find ‘b’.
The value of ‘b’ is 120.
GCF x LCM = product of the numbers 15 × 600 = 75 × b
9000 = 75b
b = 9000 ÷ 75 = 120
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.
: She loves to read number jokes and games.