What is the Greatest Common Factor of 14574 and 14578?

Greatest common factor (GCF) of 14574 and 14578 is 2.

GCF(14574,14578) = 2

We will now calculate the prime factors of 14574 and 14578, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14574 and 14578.

How to find the GCF of 14574 and 14578?

We will first find the prime factorization of 14574 and 14578. After we will calculate the factors of 14574 and 14578 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 14578

Prime factors of 14578 are 2, 37, 197. Prime factorization of 14578 in exponential form is:

14578 = 2¹ × 37¹ × 197¹

Step-3: Factors of 14574

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

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

Step-4: Factors of 14578

List of positive integer factors of 14578 that divides 14574 without a remainder.

1, 2, 37, 74, 197, 394, 7289

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14574 and 14578. The biggest common factor number is the GCF number.
So the greatest common factor 14574 and 14578 is 2.

Also check out the Least Common Multiple of 14574 and 14578