What is the Greatest Common Factor of 5629 and 5642?

Greatest common factor (GCF) of 5629 and 5642 is 13.

GCF(5629,5642) = 13

We will now calculate the prime factors of 5629 and 5642, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5629 and 5642.

How to find the GCF of 5629 and 5642?

We will first find the prime factorization of 5629 and 5642. After we will calculate the factors of 5629 and 5642 and find the biggest common factor number .

Step-1: Prime Factorization of 5629

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

5629 = 13¹ × 433¹

Step-2: Prime Factorization of 5642

Prime factors of 5642 are 2, 7, 13, 31. Prime factorization of 5642 in exponential form is:

5642 = 2¹ × 7¹ × 13¹ × 31¹

Step-3: Factors of 5629

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

1, 13, 433

Step-4: Factors of 5642

List of positive integer factors of 5642 that divides 5629 without a remainder.

1, 2, 7, 13, 14, 26, 31, 62, 91, 182, 217, 403, 434, 806, 2821

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5629 and 5642. The biggest common factor number is the GCF number.
So the greatest common factor 5629 and 5642 is 13.

Also check out the Least Common Multiple of 5629 and 5642