What is the Greatest Common Factor of 654 and 660?

Greatest common factor (GCF) of 654 and 660 is 6.

GCF(654,660) = 6

We will now calculate the prime factors of 654 and 660, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 654 and 660.

How to find the GCF of 654 and 660?

We will first find the prime factorization of 654 and 660. After we will calculate the factors of 654 and 660 and find the biggest common factor number .

Step-1: Prime Factorization of 654

Prime factors of 654 are 2, 3, 109. Prime factorization of 654 in exponential form is:

654 = 2¹ × 3¹ × 109¹

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 654

List of positive integer factors of 654 that divides 654 without a remainder.

1, 2, 3, 6, 109, 218, 327

Step-4: Factors of 660

List of positive integer factors of 660 that divides 654 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 654 and 660. The biggest common factor number is the GCF number.
So the greatest common factor 654 and 660 is 6.

Also check out the Least Common Multiple of 654 and 660