What is the Greatest Common Factor of 13664 and 13668?

Greatest common factor (GCF) of 13664 and 13668 is 4.

GCF(13664,13668) = 4

We will now calculate the prime factors of 13664 and 13668, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13664 and 13668.

How to find the GCF of 13664 and 13668?

We will first find the prime factorization of 13664 and 13668. After we will calculate the factors of 13664 and 13668 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 13668

Prime factors of 13668 are 2, 3, 17, 67. Prime factorization of 13668 in exponential form is:

13668 = 2² × 3¹ × 17¹ × 67¹

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 13668

List of positive integer factors of 13668 that divides 13664 without a remainder.

1, 2, 3, 4, 6, 12, 17, 34, 51, 67, 68, 102, 134, 201, 204, 268, 402, 804, 1139, 2278, 3417, 4556, 6834

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13664 and 13668. The biggest common factor number is the GCF number.
So the greatest common factor 13664 and 13668 is 4.

Also check out the Least Common Multiple of 13664 and 13668