What is the Greatest Common Factor of 34164 and 34176?

Greatest common factor (GCF) of 34164 and 34176 is 12.

GCF(34164,34176) = 12

We will now calculate the prime factors of 34164 and 34176, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34164 and 34176.

How to find the GCF of 34164 and 34176?

We will first find the prime factorization of 34164 and 34176. After we will calculate the factors of 34164 and 34176 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 34176

Prime factors of 34176 are 2, 3, 89. Prime factorization of 34176 in exponential form is:

34176 = 2⁷ × 3¹ × 89¹

Step-3: Factors of 34164

List of positive integer factors of 34164 that divides 34164 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

Step-4: Factors of 34176

List of positive integer factors of 34176 that divides 34164 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 89, 96, 128, 178, 192, 267, 356, 384, 534, 712, 1068, 1424, 2136, 2848, 4272, 5696, 8544, 11392, 17088

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34164 and 34176. The biggest common factor number is the GCF number.
So the greatest common factor 34164 and 34176 is 12.

Also check out the Least Common Multiple of 34164 and 34176