What is the GCF of 30 and 75?
Greatest Common Factor of two or more numbers is the largest possible number which divides the given numbers exactly without any remainder.
Answer: GCF of 30 and 75 is 15
We can find the GCF by the following methods
Methods to find GCF of 30 and 75

Prime factorization Method

Listing the common factors method

Long division Method
Method 1: GCF of 30 and 75 by Prime Factorization
Let us represent 30 and 75 as a product of its prime numbers.
Prime factorization of 30 is 2 × 3 × 5
Prime factorization of 75 is 3 × 5 × 5
Common factor = 3, 5
GCF is the product of the factors that are common to each of the given numbers.
GCF = 3 × 5 = 15
Method 2: GCF of 30 and 75 by Listing the Common Factors
Common Factors of 30 and 75 : 1, 3, 5, 15
Greatest common factor = 15
GCF of 30 and 75 is 15
Method 3: GCF of 30 and 75 by Long Division

Step 1: Divide 75 by 30 and check the remainder.

Step 2: Make the remainder of the above step as the divisor and the divisor of the above step as the dividend and perform the long division again.

Step 3: Continue till you get remainder as 0
You can find the GCF in any of the above methods but the solution will be the same.
Therefore, GCF of 30 and 75 is 15