What is the Greatest Common Factor of 5616 and 5629?

Greatest common factor (GCF) of 5616 and 5629 is 13.

GCF(5616,5629) = 13

We will now calculate the prime factors of 5616 and 5629, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5616 and 5629.

How to find the GCF of 5616 and 5629?

We will first find the prime factorization of 5616 and 5629. After we will calculate the factors of 5616 and 5629 and find the biggest common factor number .

Step-1: Prime Factorization of 5616

Prime factors of 5616 are 2, 3, 13. Prime factorization of 5616 in exponential form is:

5616 = 2⁴ × 3³ × 13¹

Step-2: Prime Factorization of 5629

Prime factors of 5629 are 13, 433. Prime factorization of 5629 in exponential form is:

5629 = 13¹ × 433¹

Step-3: Factors of 5616

List of positive integer factors of 5616 that divides 5616 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 27, 36, 39, 48, 52, 54, 72, 78, 104, 108, 117, 144, 156, 208, 216, 234, 312, 351, 432, 468, 624, 702, 936, 1404, 1872, 2808

Step-4: Factors of 5629

List of positive integer factors of 5629 that divides 5616 without a remainder.

1, 13, 433

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5616 and 5629. The biggest common factor number is the GCF number.
So the greatest common factor 5616 and 5629 is 13.

Also check out the Least Common Multiple of 5616 and 5629