What is the Greatest Common Factor of 7709 and 7722?

Greatest common factor (GCF) of 7709 and 7722 is 13.

GCF(7709,7722) = 13

We will now calculate the prime factors of 7709 and 7722, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7709 and 7722.

How to find the GCF of 7709 and 7722?

We will first find the prime factorization of 7709 and 7722. After we will calculate the factors of 7709 and 7722 and find the biggest common factor number .

Step-1: Prime Factorization of 7709

Prime factors of 7709 are 13, 593. Prime factorization of 7709 in exponential form is:

7709 = 13¹ × 593¹

Step-2: Prime Factorization of 7722

Prime factors of 7722 are 2, 3, 11, 13. Prime factorization of 7722 in exponential form is:

7722 = 2¹ × 3³ × 11¹ × 13¹

Step-3: Factors of 7709

List of positive integer factors of 7709 that divides 7709 without a remainder.

1, 13, 593

Step-4: Factors of 7722

List of positive integer factors of 7722 that divides 7709 without a remainder.

1, 2, 3, 6, 9, 11, 13, 18, 22, 26, 27, 33, 39, 54, 66, 78, 99, 117, 143, 198, 234, 286, 297, 351, 429, 594, 702, 858, 1287, 2574, 3861

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7709 and 7722. The biggest common factor number is the GCF number.
So the greatest common factor 7709 and 7722 is 13.

Also check out the Least Common Multiple of 7709 and 7722