What is the Greatest Common Factor of 19140 and 19149?

Greatest common factor (GCF) of 19140 and 19149 is 3.

GCF(19140,19149) = 3

We will now calculate the prime factors of 19140 and 19149, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19140 and 19149.

How to find the GCF of 19140 and 19149?

We will first find the prime factorization of 19140 and 19149. After we will calculate the factors of 19140 and 19149 and find the biggest common factor number .

Step-1: Prime Factorization of 19140

Prime factors of 19140 are 2, 3, 5, 11, 29. Prime factorization of 19140 in exponential form is:

19140 = 2² × 3¹ × 5¹ × 11¹ × 29¹

Step-2: Prime Factorization of 19149

Prime factors of 19149 are 3, 13, 491. Prime factorization of 19149 in exponential form is:

19149 = 3¹ × 13¹ × 491¹

Step-3: Factors of 19140

List of positive integer factors of 19140 that divides 19140 without a remainder.

1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 29, 30, 33, 44, 55, 58, 60, 66, 87, 110, 116, 132, 145, 165, 174, 220, 290, 319, 330, 348, 435, 580, 638, 660, 870, 957, 1276, 1595, 1740, 1914, 3190, 3828, 4785, 6380, 9570

Step-4: Factors of 19149

List of positive integer factors of 19149 that divides 19140 without a remainder.

1, 3, 13, 39, 491, 1473, 6383

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19140 and 19149. The biggest common factor number is the GCF number.
So the greatest common factor 19140 and 19149 is 3.

Also check out the Least Common Multiple of 19140 and 19149