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 to schedule events. In this topic, we will learn about the GCF of 30 and 75.
The greatest common factor of 30 and 75 is 15. 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.
To find the GCF of 30 and 75, a few methods are described below:
Steps to find the GCF of 30 and 75 using the listing of factors:
Step 1: Firstly, list the factors of each number:
Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30.
Factors of 75 = 1, 3, 5, 15, 25, 75.
Step 2: Now, identify the common factors of them. Common factors of 30 and 75: 1, 3, 5, 15.
Step 3: Choose the largest factor:
The largest factor that both numbers have is 15.
The GCF of 30 and 75 is 15.
To find the GCF of 30 and 75 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number:
Prime Factors of 30: 30 = 2 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 30 and 75 is 15.
Find the GCF of 30 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 30 75 ÷ 30 = 2 (quotient), The remainder is calculated as 75 − (30×2) = 15
The remainder is 15, not zero, so continue the process
Step 2: Now 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 30 and 75 is 15.
Finding GCF of 30 and 75 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
A gardener has 30 tulips and 75 roses. She wants to create bouquets with an equal number of each flower. How many flowers will each bouquet contain?
We should find the GCF of 30 and 75 GCF of 30 and 75
3 x 5 = 15.
There are 15 equal bouquets
30 ÷ 15 = 2
75 ÷ 15 = 5
There will be 15 bouquets, and each bouquet gets 2 tulips and 5 roses.
As the GCF of 30 and 75 is 15, the gardener can make 15 bouquets.
Now divide 30 and 75 by 15.
Each bouquet gets 2 tulips and 5 roses.
A chef has 30 apples and 75 oranges. He wants to arrange them in fruit baskets with the same number of each fruit in each basket. How many fruits will each basket have?
GCF of 30 and 75
3 x 5 = 15.
So each basket will have 15 fruits.
There are 30 apples and 75 oranges. To find the total number of fruits in each basket, we should find the GCF of 30 and 75. There will be 15 fruits in each basket.
A tailor has 30 meters of silk fabric and 75 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 30 and 75
The GCF of 30 and 75
3 x 5 = 15.
The fabric is 15 meters long.
For calculating the longest length of the fabric first we need to calculate the GCF of 30 and 75 which is 15.
The length of each piece of fabric will be 15 meters.
A carpenter has two wooden planks, one 30 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 30 and 75
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, 30 cm and 75 cm, respectively.
We have to find the GCF of 30 and 75, which is 15 cm.
The longest length of each piece is 15 cm.
If the GCF of 30 and ‘a’ is 15, and the LCM is 150. Find ‘a’.
The value of ‘a’ is 75.
GCF x LCM = product of the numbers
15 × 150 = 30 × a
2250 = 30a
a = 2250 ÷ 30 = 75
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.