What is the Greatest Common Factor of 34146 and 34164?

Greatest common factor (GCF) of 34146 and 34164 is 18.

GCF(34146,34164) = 18

We will now calculate the prime factors of 34146 and 34164, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34146 and 34164.

How to find the GCF of 34146 and 34164?

We will first find the prime factorization of 34146 and 34164. After we will calculate the factors of 34146 and 34164 and find the biggest common factor number .

Step-1: Prime Factorization of 34146

Prime factors of 34146 are 2, 3, 7, 271. Prime factorization of 34146 in exponential form is:

34146 = 2¹ × 3² × 7¹ × 271¹

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 34146

List of positive integer factors of 34146 that divides 34146 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126, 271, 542, 813, 1626, 1897, 2439, 3794, 4878, 5691, 11382, 17073

Step-4: Factors of 34164

List of positive integer factors of 34164 that divides 34146 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 34146 and 34164. The biggest common factor number is the GCF number.
So the greatest common factor 34146 and 34164 is 18.

Also check out the Least Common Multiple of 34146 and 34164