What is the Greatest Common Factor of 644 and 658?

Greatest common factor (GCF) of 644 and 658 is 14.

GCF(644,658) = 14

We will now calculate the prime factors of 644 and 658, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 644 and 658.

How to find the GCF of 644 and 658?

We will first find the prime factorization of 644 and 658. After we will calculate the factors of 644 and 658 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 658

Prime factors of 658 are 2, 7, 47. Prime factorization of 658 in exponential form is:

658 = 2¹ × 7¹ × 47¹

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 658

List of positive integer factors of 658 that divides 644 without a remainder.

1, 2, 7, 14, 47, 94, 329

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 644 and 658. The biggest common factor number is the GCF number.
So the greatest common factor 644 and 658 is 14.

Also check out the Least Common Multiple of 644 and 658