What is the Greatest Common Factor of 13629 and 13643?

Greatest common factor (GCF) of 13629 and 13643 is 7.

GCF(13629,13643) = 7

We will now calculate the prime factors of 13629 and 13643, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13629 and 13643.

How to find the GCF of 13629 and 13643?

We will first find the prime factorization of 13629 and 13643. After we will calculate the factors of 13629 and 13643 and find the biggest common factor number .

Step-1: Prime Factorization of 13629

Prime factors of 13629 are 3, 7, 11, 59. Prime factorization of 13629 in exponential form is:

13629 = 3¹ × 7¹ × 11¹ × 59¹

Step-2: Prime Factorization of 13643

Prime factors of 13643 are 7, 1949. Prime factorization of 13643 in exponential form is:

13643 = 7¹ × 1949¹

Step-3: Factors of 13629

List of positive integer factors of 13629 that divides 13629 without a remainder.

1, 3, 7, 11, 21, 33, 59, 77, 177, 231, 413, 649, 1239, 1947, 4543

Step-4: Factors of 13643

List of positive integer factors of 13643 that divides 13629 without a remainder.

1, 7, 1949

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13629 and 13643. The biggest common factor number is the GCF number.
So the greatest common factor 13629 and 13643 is 7.

Also check out the Least Common Multiple of 13629 and 13643