What is the Greatest Common Factor of 648 and 660?

Greatest common factor (GCF) of 648 and 660 is 12.

GCF(648,660) = 12

We will now calculate the prime factors of 648 and 660, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 648 and 660.

How to find the GCF of 648 and 660?

We will first find the prime factorization of 648 and 660. After we will calculate the factors of 648 and 660 and find the biggest common factor number .

Step-1: Prime Factorization of 648

Prime factors of 648 are 2, 3. Prime factorization of 648 in exponential form is:

648 = 2³ × 3⁴

Step-2: Prime Factorization of 660

Prime factors of 660 are 2, 3, 5, 11. Prime factorization of 660 in exponential form is:

660 = 2² × 3¹ × 5¹ × 11¹

Step-3: Factors of 648

List of positive integer factors of 648 that divides 648 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324

Step-4: Factors of 660

List of positive integer factors of 660 that divides 648 without a remainder.

1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 648 and 660. The biggest common factor number is the GCF number.
So the greatest common factor 648 and 660 is 12.

Also check out the Least Common Multiple of 648 and 660