What is the Greatest Common Factor of 639 and 654?

Greatest common factor (GCF) of 639 and 654 is 3.

GCF(639,654) = 3

We will now calculate the prime factors of 639 and 654, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 639 and 654.

How to find the GCF of 639 and 654?

We will first find the prime factorization of 639 and 654. After we will calculate the factors of 639 and 654 and find the biggest common factor number .

Step-1: Prime Factorization of 639

Prime factors of 639 are 3, 71. Prime factorization of 639 in exponential form is:

639 = 3² × 71¹

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 639

List of positive integer factors of 639 that divides 639 without a remainder.

1, 3, 9, 71, 213

Step-4: Factors of 654

List of positive integer factors of 654 that divides 639 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 639 and 654. The biggest common factor number is the GCF number.
So the greatest common factor 639 and 654 is 3.

Also check out the Least Common Multiple of 639 and 654