What is the Greatest Common Factor of 11564 and 11578?

Greatest common factor (GCF) of 11564 and 11578 is 14.

GCF(11564,11578) = 14

We will now calculate the prime factors of 11564 and 11578, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 11564 and 11578.

How to find the GCF of 11564 and 11578?

We will first find the prime factorization of 11564 and 11578. After we will calculate the factors of 11564 and 11578 and find the biggest common factor number .

Step-1: Prime Factorization of 11564

Prime factors of 11564 are 2, 7, 59. Prime factorization of 11564 in exponential form is:

11564 = 2² × 7² × 59¹

Step-2: Prime Factorization of 11578

Prime factors of 11578 are 2, 7, 827. Prime factorization of 11578 in exponential form is:

11578 = 2¹ × 7¹ × 827¹

Step-3: Factors of 11564

List of positive integer factors of 11564 that divides 11564 without a remainder.

1, 2, 4, 7, 14, 28, 49, 59, 98, 118, 196, 236, 413, 826, 1652, 2891, 5782

Step-4: Factors of 11578

List of positive integer factors of 11578 that divides 11564 without a remainder.

1, 2, 7, 14, 827, 1654, 5789

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 11564 and 11578. The biggest common factor number is the GCF number.
So the greatest common factor 11564 and 11578 is 14.

Also check out the Least Common Multiple of 11564 and 11578