What is the Greatest Common Factor of 13664 and 13671?

Greatest common factor (GCF) of 13664 and 13671 is 7.

GCF(13664,13671) = 7

We will now calculate the prime factors of 13664 and 13671, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13664 and 13671.

How to find the GCF of 13664 and 13671?

We will first find the prime factorization of 13664 and 13671. After we will calculate the factors of 13664 and 13671 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 13671

Prime factors of 13671 are 3, 7, 31. Prime factorization of 13671 in exponential form is:

13671 = 3² × 7² × 31¹

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 13671

List of positive integer factors of 13671 that divides 13664 without a remainder.

1, 3, 7, 9, 21, 31, 49, 63, 93, 147, 217, 279, 441, 651, 1519, 1953, 4557

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13664 and 13671. The biggest common factor number is the GCF number.
So the greatest common factor 13664 and 13671 is 7.

Also check out the Least Common Multiple of 13664 and 13671