What is the GCF of 14 and 21?
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 14 and 21 is 7
We can find the GCF by the following methods
Methods to find GCF of 14 and 21
Prime factorization Method
Listing the common factors method
Long division Method
Method 1: GCF of 14 and 21 by Prime Factorization
Let us represent 14 and 21 as a product of its prime numbers.
Prime factorization of 14 is 2 × 7
Prime factorization of 21 is 3 × 7
Common factors = 7
GCF is the product of the factors that are common to each of the given numbers.
GCF is 7
Method 2: GCF of 14 and 21 by Listing the Common Factors
Common Factors of 14 and 21: 1, 7
Greatest common factor = 7
GCF of 14 and 21 is 7
Method 3: GCF of 14 and 21 by Long Division
Step 1: Divide 21 by 14 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.