What is the Greatest Common Factor of 19140 and 19160?

Greatest common factor (GCF) of 19140 and 19160 is 20.

GCF(19140,19160) = 20

We will now calculate the prime factors of 19140 and 19160, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19140 and 19160.

How to find the GCF of 19140 and 19160?

We will first find the prime factorization of 19140 and 19160. After we will calculate the factors of 19140 and 19160 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 19160

Prime factors of 19160 are 2, 5, 479. Prime factorization of 19160 in exponential form is:

19160 = 2³ × 5¹ × 479¹

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 19160

List of positive integer factors of 19160 that divides 19140 without a remainder.

1, 2, 4, 5, 8, 10, 20, 40, 479, 958, 1916, 2395, 3832, 4790, 9580

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19140 and 19160. The biggest common factor number is the GCF number.
So the greatest common factor 19140 and 19160 is 20.

Also check out the Least Common Multiple of 19140 and 19160