What is the Greatest Common Factor of 13657 and 13664?

Greatest common factor (GCF) of 13657 and 13664 is 7.

GCF(13657,13664) = 7

We will now calculate the prime factors of 13657 and 13664, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13657 and 13664.

How to find the GCF of 13657 and 13664?

We will first find the prime factorization of 13657 and 13664. After we will calculate the factors of 13657 and 13664 and find the biggest common factor number .

Step-1: Prime Factorization of 13657

Prime factors of 13657 are 7, 1951. Prime factorization of 13657 in exponential form is:

13657 = 7¹ × 1951¹

Step-2: 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-3: Factors of 13657

List of positive integer factors of 13657 that divides 13657 without a remainder.

1, 7, 1951

Step-4: Factors of 13664

List of positive integer factors of 13664 that divides 13657 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13657 and 13664. The biggest common factor number is the GCF number.
So the greatest common factor 13657 and 13664 is 7.

Also check out the Least Common Multiple of 13657 and 13664