What is the Greatest Common Factor of 13566 and 13574?

Greatest common factor (GCF) of 13566 and 13574 is 2.

GCF(13566,13574) = 2

We will now calculate the prime factors of 13566 and 13574, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13566 and 13574.

How to find the GCF of 13566 and 13574?

We will first find the prime factorization of 13566 and 13574. After we will calculate the factors of 13566 and 13574 and find the biggest common factor number .

Step-1: Prime Factorization of 13566

Prime factors of 13566 are 2, 3, 7, 17, 19. Prime factorization of 13566 in exponential form is:

13566 = 2¹ × 3¹ × 7¹ × 17¹ × 19¹

Step-2: 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-3: Factors of 13566

List of positive integer factors of 13566 that divides 13566 without a remainder.

1, 2, 3, 6, 7, 14, 17, 19, 21, 34, 38, 42, 51, 57, 102, 114, 119, 133, 238, 266, 323, 357, 399, 646, 714, 798, 969, 1938, 2261, 4522, 6783

Step-4: Factors of 13574

List of positive integer factors of 13574 that divides 13566 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13566 and 13574. The biggest common factor number is the GCF number.
So the greatest common factor 13566 and 13574 is 2.

Also check out the Least Common Multiple of 13566 and 13574