What is the Greatest Common Factor of 54 and 72?
Greatest common factor (GCF) of 54 and 72 is 18.
GCF(54,72) = 18
We will now calculate the prime factors of 54 and 72, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54 and 72.
How to find the GCF of 54 and 72?
We will first find the prime factorization of 54 and 72. After we will calculate the factors of 54 and 72 and find the biggest common factor number .
Step-1: Prime Factorization of 54
Prime factors of 54 are 2, 3. Prime factorization of 54 in exponential form is:
54 = 21 × 33
Step-2: Prime Factorization of 72
Prime factors of 72 are 2, 3. Prime factorization of 72 in exponential form is:
72 = 23 × 32
Step-3: Factors of 54
List of positive integer factors of 54 that divides 54 without a remainder.
1, 2, 3, 6, 9, 18, 27
Step-4: Factors of 72
List of positive integer factors of 72 that divides 54 without a remainder.
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36
Final Step: Biggest Common Factor Number
We found the factors and prime factorization of 54 and 72. The biggest common factor number is the GCF number.
So the greatest common factor 54 and 72 is 18.
Also check out the Least Common Multiple of 54 and 72