What is the Greatest Common Factor of 609 and 623?

Greatest common factor (GCF) of 609 and 623 is 7.

GCF(609,623) = 7

We will now calculate the prime factors of 609 and 623, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 609 and 623.

How to find the GCF of 609 and 623?

We will first find the prime factorization of 609 and 623. After we will calculate the factors of 609 and 623 and find the biggest common factor number .

Step-1: Prime Factorization of 609

Prime factors of 609 are 3, 7, 29. Prime factorization of 609 in exponential form is:

609 = 3¹ × 7¹ × 29¹

Step-2: Prime Factorization of 623

Prime factors of 623 are 7, 89. Prime factorization of 623 in exponential form is:

623 = 7¹ × 89¹

Step-3: Factors of 609

List of positive integer factors of 609 that divides 609 without a remainder.

1, 3, 7, 21, 29, 87, 203

Step-4: Factors of 623

List of positive integer factors of 623 that divides 609 without a remainder.

1, 7, 89

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 609 and 623. The biggest common factor number is the GCF number.
So the greatest common factor 609 and 623 is 7.

Also check out the Least Common Multiple of 609 and 623