What is the Greatest Common Factor of 25564 and 25578?

Greatest common factor (GCF) of 25564 and 25578 is 14.

GCF(25564,25578) = 14

We will now calculate the prime factors of 25564 and 25578, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25564 and 25578.

How to find the GCF of 25564 and 25578?

We will first find the prime factorization of 25564 and 25578. After we will calculate the factors of 25564 and 25578 and find the biggest common factor number .

Step-1: Prime Factorization of 25564

Prime factors of 25564 are 2, 7, 11, 83. Prime factorization of 25564 in exponential form is:

25564 = 2² × 7¹ × 11¹ × 83¹

Step-2: Prime Factorization of 25578

Prime factors of 25578 are 2, 3, 7, 29. Prime factorization of 25578 in exponential form is:

25578 = 2¹ × 3² × 7² × 29¹

Step-3: Factors of 25564

List of positive integer factors of 25564 that divides 25564 without a remainder.

1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 83, 154, 166, 308, 332, 581, 913, 1162, 1826, 2324, 3652, 6391, 12782

Step-4: Factors of 25578

List of positive integer factors of 25578 that divides 25564 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 29, 42, 49, 58, 63, 87, 98, 126, 147, 174, 203, 261, 294, 406, 441, 522, 609, 882, 1218, 1421, 1827, 2842, 3654, 4263, 8526, 12789

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25564 and 25578. The biggest common factor number is the GCF number.
So the greatest common factor 25564 and 25578 is 14.

Also check out the Least Common Multiple of 25564 and 25578