What is the Greatest Common Factor of 1350 and 1365?

Greatest common factor (GCF) of 1350 and 1365 is 15.

GCF(1350,1365) = 15

We will now calculate the prime factors of 1350 and 1365, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1350 and 1365.

How to find the GCF of 1350 and 1365?

We will first find the prime factorization of 1350 and 1365. After we will calculate the factors of 1350 and 1365 and find the biggest common factor number .

Step-1: Prime Factorization of 1350

Prime factors of 1350 are 2, 3, 5. Prime factorization of 1350 in exponential form is:

1350 = 2¹ × 3³ × 5²

Step-2: 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-3: Factors of 1350

List of positive integer factors of 1350 that divides 1350 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 27, 30, 45, 50, 54, 75, 90, 135, 150, 225, 270, 450, 675

Step-4: Factors of 1365

List of positive integer factors of 1365 that divides 1350 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1350 and 1365. The biggest common factor number is the GCF number.
So the greatest common factor 1350 and 1365 is 15.

Also check out the Least Common Multiple of 1350 and 1365