What is the Greatest Common Factor of 1365 and 1380?

Greatest common factor (GCF) of 1365 and 1380 is 15.

GCF(1365,1380) = 15

We will now calculate the prime factors of 1365 and 1380, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1365 and 1380.

How to find the GCF of 1365 and 1380?

We will first find the prime factorization of 1365 and 1380. After we will calculate the factors of 1365 and 1380 and find the biggest common factor number .

Step-1: Prime Factorization of 1365

Prime factors of 1365 are 3, 5, 7, 13. Prime factorization of 1365 in exponential form is:

1365 = 3¹ × 5¹ × 7¹ × 13¹

Step-2: Prime Factorization of 1380

Prime factors of 1380 are 2, 3, 5, 23. Prime factorization of 1380 in exponential form is:

1380 = 2² × 3¹ × 5¹ × 23¹

Step-3: Factors of 1365

List of positive integer factors of 1365 that divides 1365 without a remainder.

1, 3, 5, 7, 13, 15, 21, 35, 39, 65, 91, 105, 195, 273, 455

Step-4: Factors of 1380

List of positive integer factors of 1380 that divides 1365 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 23, 30, 46, 60, 69, 92, 115, 138, 230, 276, 345, 460, 690

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1365 and 1380. The biggest common factor number is the GCF number.
So the greatest common factor 1365 and 1380 is 15.

Also check out the Least Common Multiple of 1365 and 1380