What is the Greatest Common Factor of 5305 and 5320?

Greatest common factor (GCF) of 5305 and 5320 is 5.

GCF(5305,5320) = 5

We will now calculate the prime factors of 5305 and 5320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5305 and 5320.

How to find the GCF of 5305 and 5320?

We will first find the prime factorization of 5305 and 5320. After we will calculate the factors of 5305 and 5320 and find the biggest common factor number .

Step-1: Prime Factorization of 5305

Prime factors of 5305 are 5, 1061. Prime factorization of 5305 in exponential form is:

5305 = 5¹ × 1061¹

Step-2: Prime Factorization of 5320

Prime factors of 5320 are 2, 5, 7, 19. Prime factorization of 5320 in exponential form is:

5320 = 2³ × 5¹ × 7¹ × 19¹

Step-3: Factors of 5305

List of positive integer factors of 5305 that divides 5305 without a remainder.

1, 5, 1061

Step-4: Factors of 5320

List of positive integer factors of 5320 that divides 5305 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 19, 20, 28, 35, 38, 40, 56, 70, 76, 95, 133, 140, 152, 190, 266, 280, 380, 532, 665, 760, 1064, 1330, 2660

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5305 and 5320. The biggest common factor number is the GCF number.
So the greatest common factor 5305 and 5320 is 5.

Also check out the Least Common Multiple of 5305 and 5320