What is the GCF of 21 and 30?
Greatest Common Factor is a greatest number that is a factor of two or more other numbers.
The GCF (greatest common factor) is the same as: HCF (Highest Common Factor), GCD (Greatest Common Divisor), HCD (Highest Common Divisor), GCM (Greatest Common Measure), HCM (Highest Common Measure)
Answer: GCF of 21 and 30 is 3
Two methods to find the GCF of 21 and 30 are explained below.
Methods to find GCF of 21 and 30
- Prime Factorization
- Long Division
Method 1: GCF of 21 and 30 by Prime Factorization
GCF is the product of the factors that are common to each of the given numbers.
Prime factorization of 21 is 3 × 7
Prime factorization of 30 is 2 × 3 × 5
The occurrences of common prime factors of 21 and 30 is 3
Hence GCF(21, 30) = 3
Method 2: GCF of 21 and 30 by Long Division
- Step 1: Divide the larger number by the smaller
- Step 2: Divide the dividend by the remainder obtained in step 1 and repeat this step until we get the remainder as 0
- Step 3: The last dividend is the GCF of the two numbers
We take the larger value 30 as dividend and smaller value 21 as divisor
We will get the GCF same for the given numbers by using different methods.