What is the Greatest Common Factor of 644 and 654?

Greatest common factor (GCF) of 644 and 654 is 2.

GCF(644,654) = 2

We will now calculate the prime factors of 644 and 654, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 644 and 654.

How to find the GCF of 644 and 654?

We will first find the prime factorization of 644 and 654. After we will calculate the factors of 644 and 654 and find the biggest common factor number .

Step-1: Prime Factorization of 644

Prime factors of 644 are 2, 7, 23. Prime factorization of 644 in exponential form is:

644 = 2² × 7¹ × 23¹

Step-2: 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-3: Factors of 644

List of positive integer factors of 644 that divides 644 without a remainder.

1, 2, 4, 7, 14, 23, 28, 46, 92, 161, 322

Step-4: Factors of 654

List of positive integer factors of 654 that divides 644 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 644 and 654. The biggest common factor number is the GCF number.
So the greatest common factor 644 and 654 is 2.

Also check out the Least Common Multiple of 644 and 654