What is the Greatest Common Factor of 14574 and 14580?

Greatest common factor (GCF) of 14574 and 14580 is 6.

GCF(14574,14580) = 6

We will now calculate the prime factors of 14574 and 14580, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14574 and 14580.

How to find the GCF of 14574 and 14580?

We will first find the prime factorization of 14574 and 14580. After we will calculate the factors of 14574 and 14580 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 14580

Prime factors of 14580 are 2, 3, 5. Prime factorization of 14580 in exponential form is:

14580 = 2² × 3⁶ × 5¹

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 14580

List of positive integer factors of 14580 that divides 14574 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 81, 90, 108, 135, 162, 180, 243, 270, 324, 405, 486, 540, 729, 810, 972, 1215, 1458, 1620, 2430, 2916, 3645, 4860, 7290

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14574 and 14580. The biggest common factor number is the GCF number.
So the greatest common factor 14574 and 14580 is 6.

Also check out the Least Common Multiple of 14574 and 14580