What is the GCF of 27 and 72?
Greatest Common Factor is the 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 27 and 72 is 9
Two methods to find the GCF of 27 and 72 are explained below.
Methods to find GCF of 27 and 72
- Prime Factorization
- Long Division
Method 1: GCF of 27 and 72 by Prime Factorization
GCF is the product of the factors that are common to each of the given numbers.
Prime factorization of 27 is 3 × 3 × 3
Prime factorization of 72 is 2 × 2 × 2 × 3 × 3
The occurrences of common prime factors of 27 and 72 are 3 and 3
Hence GCF(27, 72) is 3 × 3 = 9
Method 2: GCF of 27 and 72 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 72 as dividend and smaller value 27 as the divisor
We will get the GCF same for the given numbers by using different methods.