What is the Greatest Common Factor of 14564 and 14574?

Greatest common factor (GCF) of 14564 and 14574 is 2.

GCF(14564,14574) = 2

We will now calculate the prime factors of 14564 and 14574, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14564 and 14574.

How to find the GCF of 14564 and 14574?

We will first find the prime factorization of 14564 and 14574. After we will calculate the factors of 14564 and 14574 and find the biggest common factor number .

Step-1: Prime Factorization of 14564

Prime factors of 14564 are 2, 11, 331. Prime factorization of 14564 in exponential form is:

14564 = 2² × 11¹ × 331¹

Step-2: Prime Factorization of 14574

Prime factors of 14574 are 2, 3, 7, 347. Prime factorization of 14574 in exponential form is:

14574 = 2¹ × 3¹ × 7¹ × 347¹

Step-3: Factors of 14564

List of positive integer factors of 14564 that divides 14564 without a remainder.

1, 2, 4, 11, 22, 44, 331, 662, 1324, 3641, 7282

Step-4: Factors of 14574

List of positive integer factors of 14574 that divides 14564 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 347, 694, 1041, 2082, 2429, 4858, 7287

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14564 and 14574. The biggest common factor number is the GCF number.
So the greatest common factor 14564 and 14574 is 2.

Also check out the Least Common Multiple of 14564 and 14574