What is the Greatest Common Factor of 14574 and 14582?

Greatest common factor (GCF) of 14574 and 14582 is 2.

GCF(14574,14582) = 2

We will now calculate the prime factors of 14574 and 14582, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14574 and 14582.

How to find the GCF of 14574 and 14582?

We will first find the prime factorization of 14574 and 14582. After we will calculate the factors of 14574 and 14582 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 14582

Prime factors of 14582 are 2, 23, 317. Prime factorization of 14582 in exponential form is:

14582 = 2¹ × 23¹ × 317¹

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 14582

List of positive integer factors of 14582 that divides 14574 without a remainder.

1, 2, 23, 46, 317, 634, 7291

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14574 and 14582. The biggest common factor number is the GCF number.
So the greatest common factor 14574 and 14582 is 2.

Also check out the Least Common Multiple of 14574 and 14582