What is the Greatest Common Factor of 13574 and 13585?

Greatest common factor (GCF) of 13574 and 13585 is 11.

GCF(13574,13585) = 11

We will now calculate the prime factors of 13574 and 13585, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13574 and 13585.

How to find the GCF of 13574 and 13585?

We will first find the prime factorization of 13574 and 13585. After we will calculate the factors of 13574 and 13585 and find the biggest common factor number .

Step-1: Prime Factorization of 13574

Prime factors of 13574 are 2, 11, 617. Prime factorization of 13574 in exponential form is:

13574 = 2¹ × 11¹ × 617¹

Step-2: 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-3: Factors of 13574

List of positive integer factors of 13574 that divides 13574 without a remainder.

1, 2, 11, 22, 617, 1234, 6787

Step-4: Factors of 13585

List of positive integer factors of 13585 that divides 13574 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13574 and 13585. The biggest common factor number is the GCF number.
So the greatest common factor 13574 and 13585 is 11.

Also check out the Least Common Multiple of 13574 and 13585