What is the Greatest Common Factor of 13585 and 13598?

Greatest common factor (GCF) of 13585 and 13598 is 13.

GCF(13585,13598) = 13

We will now calculate the prime factors of 13585 and 13598, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13585 and 13598.

How to find the GCF of 13585 and 13598?

We will first find the prime factorization of 13585 and 13598. After we will calculate the factors of 13585 and 13598 and find the biggest common factor number .

Step-1: Prime Factorization of 13585

Prime factors of 13585 are 5, 11, 13, 19. Prime factorization of 13585 in exponential form is:

13585 = 5¹ × 11¹ × 13¹ × 19¹

Step-2: Prime Factorization of 13598

Prime factors of 13598 are 2, 13, 523. Prime factorization of 13598 in exponential form is:

13598 = 2¹ × 13¹ × 523¹

Step-3: Factors of 13585

List of positive integer factors of 13585 that divides 13585 without a remainder.

1, 5, 11, 13, 19, 55, 65, 95, 143, 209, 247, 715, 1045, 1235, 2717

Step-4: Factors of 13598

List of positive integer factors of 13598 that divides 13585 without a remainder.

1, 2, 13, 26, 523, 1046, 6799

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13585 and 13598. The biggest common factor number is the GCF number.
So the greatest common factor 13585 and 13598 is 13.

Also check out the Least Common Multiple of 13585 and 13598