What is the Greatest Common Factor of 642 and 657?

Greatest common factor (GCF) of 642 and 657 is 3.

GCF(642,657) = 3

We will now calculate the prime factors of 642 and 657, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 642 and 657.

How to find the GCF of 642 and 657?

We will first find the prime factorization of 642 and 657. After we will calculate the factors of 642 and 657 and find the biggest common factor number .

Step-1: Prime Factorization of 642

Prime factors of 642 are 2, 3, 107. Prime factorization of 642 in exponential form is:

642 = 2¹ × 3¹ × 107¹

Step-2: Prime Factorization of 657

Prime factors of 657 are 3, 73. Prime factorization of 657 in exponential form is:

657 = 3² × 73¹

Step-3: Factors of 642

List of positive integer factors of 642 that divides 642 without a remainder.

1, 2, 3, 6, 107, 214, 321

Step-4: Factors of 657

List of positive integer factors of 657 that divides 642 without a remainder.

1, 3, 9, 73, 219

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 642 and 657. The biggest common factor number is the GCF number.
So the greatest common factor 642 and 657 is 3.

Also check out the Least Common Multiple of 642 and 657