What is the Greatest Common Factor of 13585 and 13600?

Greatest common factor (GCF) of 13585 and 13600 is 5.

GCF(13585,13600) = 5

We will now calculate the prime factors of 13585 and 13600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13585 and 13600.

How to find the GCF of 13585 and 13600?

We will first find the prime factorization of 13585 and 13600. After we will calculate the factors of 13585 and 13600 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 13600

Prime factors of 13600 are 2, 5, 17. Prime factorization of 13600 in exponential form is:

13600 = 2⁵ × 5² × 17¹

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 13600

List of positive integer factors of 13600 that divides 13585 without a remainder.

1, 2, 4, 5, 8, 10, 16, 17, 20, 25, 32, 34, 40, 50, 68, 80, 85, 100, 136, 160, 170, 200, 272, 340, 400, 425, 544, 680, 800, 850, 1360, 1700, 2720, 3400, 6800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13585 and 13600. The biggest common factor number is the GCF number.
So the greatest common factor 13585 and 13600 is 5.

Also check out the Least Common Multiple of 13585 and 13600