What is the Greatest Common Factor of 34149 and 34164?

Greatest common factor (GCF) of 34149 and 34164 is 3.

GCF(34149,34164) = 3

We will now calculate the prime factors of 34149 and 34164, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34149 and 34164.

How to find the GCF of 34149 and 34164?

We will first find the prime factorization of 34149 and 34164. After we will calculate the factors of 34149 and 34164 and find the biggest common factor number .

Step-1: Prime Factorization of 34149

Prime factors of 34149 are 3, 11383. Prime factorization of 34149 in exponential form is:

34149 = 3¹ × 11383¹

Step-2: Prime Factorization of 34164

Prime factors of 34164 are 2, 3, 13, 73. Prime factorization of 34164 in exponential form is:

34164 = 2² × 3² × 13¹ × 73¹

Step-3: Factors of 34149

List of positive integer factors of 34149 that divides 34149 without a remainder.

1, 3, 11383

Step-4: Factors of 34164

List of positive integer factors of 34164 that divides 34149 without a remainder.

1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 73, 78, 117, 146, 156, 219, 234, 292, 438, 468, 657, 876, 949, 1314, 1898, 2628, 2847, 3796, 5694, 8541, 11388, 17082

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34149 and 34164. The biggest common factor number is the GCF number.
So the greatest common factor 34149 and 34164 is 3.

Also check out the Least Common Multiple of 34149 and 34164