What is the Greatest Common Factor of 654 and 674?

Greatest common factor (GCF) of 654 and 674 is 2.

GCF(654,674) = 2

We will now calculate the prime factors of 654 and 674, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 654 and 674.

How to find the GCF of 654 and 674?

We will first find the prime factorization of 654 and 674. After we will calculate the factors of 654 and 674 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 674

Prime factors of 674 are 2, 337. Prime factorization of 674 in exponential form is:

674 = 2¹ × 337¹

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 674

List of positive integer factors of 674 that divides 654 without a remainder.

1, 2, 337

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 654 and 674. The biggest common factor number is the GCF number.
So the greatest common factor 654 and 674 is 2.

Also check out the Least Common Multiple of 654 and 674