What is the Greatest Common Factor of 13664 and 13674?

Greatest common factor (GCF) of 13664 and 13674 is 2.

GCF(13664,13674) = 2

We will now calculate the prime factors of 13664 and 13674, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13664 and 13674.

How to find the GCF of 13664 and 13674?

We will first find the prime factorization of 13664 and 13674. After we will calculate the factors of 13664 and 13674 and find the biggest common factor number .

Step-1: Prime Factorization of 13664

Prime factors of 13664 are 2, 7, 61. Prime factorization of 13664 in exponential form is:

13664 = 2⁵ × 7¹ × 61¹

Step-2: Prime Factorization of 13674

Prime factors of 13674 are 2, 3, 43, 53. Prime factorization of 13674 in exponential form is:

13674 = 2¹ × 3¹ × 43¹ × 53¹

Step-3: Factors of 13664

List of positive integer factors of 13664 that divides 13664 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 61, 112, 122, 224, 244, 427, 488, 854, 976, 1708, 1952, 3416, 6832

Step-4: Factors of 13674

List of positive integer factors of 13674 that divides 13664 without a remainder.

1, 2, 3, 6, 43, 53, 86, 106, 129, 159, 258, 318, 2279, 4558, 6837

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13664 and 13674. The biggest common factor number is the GCF number.
So the greatest common factor 13664 and 13674 is 2.

Also check out the Least Common Multiple of 13664 and 13674