What is the Greatest Common Factor of 10365 and 10380?

Greatest common factor (GCF) of 10365 and 10380 is 15.

GCF(10365,10380) = 15

We will now calculate the prime factors of 10365 and 10380, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10365 and 10380.

How to find the GCF of 10365 and 10380?

We will first find the prime factorization of 10365 and 10380. After we will calculate the factors of 10365 and 10380 and find the biggest common factor number .

Step-1: Prime Factorization of 10365

Prime factors of 10365 are 3, 5, 691. Prime factorization of 10365 in exponential form is:

10365 = 3¹ × 5¹ × 691¹

Step-2: Prime Factorization of 10380

Prime factors of 10380 are 2, 3, 5, 173. Prime factorization of 10380 in exponential form is:

10380 = 2² × 3¹ × 5¹ × 173¹

Step-3: Factors of 10365

List of positive integer factors of 10365 that divides 10365 without a remainder.

1, 3, 5, 15, 691, 2073, 3455

Step-4: Factors of 10380

List of positive integer factors of 10380 that divides 10365 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 173, 346, 519, 692, 865, 1038, 1730, 2076, 2595, 3460, 5190

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10365 and 10380. The biggest common factor number is the GCF number.
So the greatest common factor 10365 and 10380 is 15.

Also check out the Least Common Multiple of 10365 and 10380