What is the GCF of 10 and 15?
The largest possible number which divides the given numbers exactly without any remainder is called Greatest Common Factor
Answer: GCF of 10 and 15 is 5
Two methods to find the GCF of 10 and 15 are explained below.
Methods to find GCF of 10 and 15
Prime factorization Method
Listing the common factors method
Method1: Find the GCF of 10 and 15 by Prime Factorization
Prime factorization of 10 is 2 × 5
Prime factorization of 15 is 3 × 15
The greatest common factor, in short, GCF is the product of the common prime factors of the given numbers.
Method2: GCF of 10 and 15 by Listing the Common Factors
1, 2, 5, and 10 are the factors of 10.
1, 3, 5, and 15 are the factors of 15
The only common factor of 10 and 15 is 5
So, GCF of 10 and 15 is 5
Method3: The GCF of 10 and 15 by Long Division
- Divide 15 by 10
- As the remainder is non-zero proceed to the next step.
- The remainder of the above step is the divisor and the divisor of the above step is the dividend.
- Continue the long division till you get the remainder as 0.
- The divisor when the remainder is 0 is the HCF of 10 and 15.
GCF is independent of the method we choose.
GCF of 10 and 15 is always 5 irrespective of how we calculate.