What is the Greatest Common Factor of 1365 and 1374?

Greatest common factor (GCF) of 1365 and 1374 is 3.

GCF(1365,1374) = 3

We will now calculate the prime factors of 1365 and 1374, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1365 and 1374.

How to find the GCF of 1365 and 1374?

We will first find the prime factorization of 1365 and 1374. After we will calculate the factors of 1365 and 1374 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 1374

Prime factors of 1374 are 2, 3, 229. Prime factorization of 1374 in exponential form is:

1374 = 2¹ × 3¹ × 229¹

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 1374

List of positive integer factors of 1374 that divides 1365 without a remainder.

1, 2, 3, 6, 229, 458, 687

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1365 and 1374. The biggest common factor number is the GCF number.
So the greatest common factor 1365 and 1374 is 3.

Also check out the Least Common Multiple of 1365 and 1374