What is the Greatest Common Factor of 13566 and 13583?

Greatest common factor (GCF) of 13566 and 13583 is 17.

GCF(13566,13583) = 17

We will now calculate the prime factors of 13566 and 13583, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13566 and 13583.

How to find the GCF of 13566 and 13583?

We will first find the prime factorization of 13566 and 13583. After we will calculate the factors of 13566 and 13583 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 13583

Prime factors of 13583 are 17, 47. Prime factorization of 13583 in exponential form is:

13583 = 17² × 47¹

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 13583

List of positive integer factors of 13583 that divides 13566 without a remainder.

1, 17, 47, 289, 799

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13566 and 13583. The biggest common factor number is the GCF number.
So the greatest common factor 13566 and 13583 is 17.

Also check out the Least Common Multiple of 13566 and 13583