What is the Greatest Common Factor of 1309 and 1320?

Greatest common factor (GCF) of 1309 and 1320 is 11.

GCF(1309,1320) = 11

We will now calculate the prime factors of 1309 and 1320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1309 and 1320.

How to find the GCF of 1309 and 1320?

We will first find the prime factorization of 1309 and 1320. After we will calculate the factors of 1309 and 1320 and find the biggest common factor number .

Step-1: Prime Factorization of 1309

Prime factors of 1309 are 7, 11, 17. Prime factorization of 1309 in exponential form is:

1309 = 7¹ × 11¹ × 17¹

Step-2: Prime Factorization of 1320

Prime factors of 1320 are 2, 3, 5, 11. Prime factorization of 1320 in exponential form is:

1320 = 2³ × 3¹ × 5¹ × 11¹

Step-3: Factors of 1309

List of positive integer factors of 1309 that divides 1309 without a remainder.

1, 7, 11, 17, 77, 119, 187

Step-4: Factors of 1320

List of positive integer factors of 1320 that divides 1309 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 24, 30, 33, 40, 44, 55, 60, 66, 88, 110, 120, 132, 165, 220, 264, 330, 440, 660

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1309 and 1320. The biggest common factor number is the GCF number.
So the greatest common factor 1309 and 1320 is 11.

Also check out the Least Common Multiple of 1309 and 1320