What is the Greatest Common Factor of 365 and 385?

Greatest common factor (GCF) of 365 and 385 is 5.

GCF(365,385) = 5

We will now calculate the prime factors of 365 and 385, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 365 and 385.

How to find the GCF of 365 and 385?

We will first find the prime factorization of 365 and 385. After we will calculate the factors of 365 and 385 and find the biggest common factor number .

Step-1: Prime Factorization of 365

Prime factors of 365 are 5, 73. Prime factorization of 365 in exponential form is:

365 = 5¹ × 73¹

Step-2: Prime Factorization of 385

Prime factors of 385 are 5, 7, 11. Prime factorization of 385 in exponential form is:

385 = 5¹ × 7¹ × 11¹

Step-3: Factors of 365

List of positive integer factors of 365 that divides 365 without a remainder.

1, 5, 73

Step-4: Factors of 385

List of positive integer factors of 385 that divides 365 without a remainder.

1, 5, 7, 11, 35, 55, 77

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 365 and 385. The biggest common factor number is the GCF number.
So the greatest common factor 365 and 385 is 5.

Also check out the Least Common Multiple of 365 and 385