What is the Greatest Common Factor of 19149 and 19164?

Greatest common factor (GCF) of 19149 and 19164 is 3.

GCF(19149,19164) = 3

We will now calculate the prime factors of 19149 and 19164, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19149 and 19164.

How to find the GCF of 19149 and 19164?

We will first find the prime factorization of 19149 and 19164. After we will calculate the factors of 19149 and 19164 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 19164

Prime factors of 19164 are 2, 3, 1597. Prime factorization of 19164 in exponential form is:

19164 = 2² × 3¹ × 1597¹

Step-3: Factors of 19149

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

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

Step-4: Factors of 19164

List of positive integer factors of 19164 that divides 19149 without a remainder.

1, 2, 3, 4, 6, 12, 1597, 3194, 4791, 6388, 9582

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19149 and 19164. The biggest common factor number is the GCF number.
So the greatest common factor 19149 and 19164 is 3.

Also check out the Least Common Multiple of 19149 and 19164