What is the Greatest Common Factor of 10164 and 10176?

Greatest common factor (GCF) of 10164 and 10176 is 12.

GCF(10164,10176) = 12

We will now calculate the prime factors of 10164 and 10176, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10164 and 10176.

How to find the GCF of 10164 and 10176?

We will first find the prime factorization of 10164 and 10176. After we will calculate the factors of 10164 and 10176 and find the biggest common factor number .

Step-1: Prime Factorization of 10164

Prime factors of 10164 are 2, 3, 7, 11. Prime factorization of 10164 in exponential form is:

10164 = 2² × 3¹ × 7¹ × 11²

Step-2: Prime Factorization of 10176

Prime factors of 10176 are 2, 3, 53. Prime factorization of 10176 in exponential form is:

10176 = 2⁶ × 3¹ × 53¹

Step-3: Factors of 10164

List of positive integer factors of 10164 that divides 10164 without a remainder.

1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 66, 77, 84, 121, 132, 154, 231, 242, 308, 363, 462, 484, 726, 847, 924, 1452, 1694, 2541, 3388, 5082

Step-4: Factors of 10176

List of positive integer factors of 10176 that divides 10164 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 53, 64, 96, 106, 159, 192, 212, 318, 424, 636, 848, 1272, 1696, 2544, 3392, 5088

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10164 and 10176. The biggest common factor number is the GCF number.
So the greatest common factor 10164 and 10176 is 12.

Also check out the Least Common Multiple of 10164 and 10176