What is the Greatest Common Factor of 10149 and 10164?

Greatest common factor (GCF) of 10149 and 10164 is 3.

GCF(10149,10164) = 3

We will now calculate the prime factors of 10149 and 10164, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10149 and 10164.

How to find the GCF of 10149 and 10164?

We will first find the prime factorization of 10149 and 10164. After we will calculate the factors of 10149 and 10164 and find the biggest common factor number .

Step-1: Prime Factorization of 10149

Prime factors of 10149 are 3, 17, 199. Prime factorization of 10149 in exponential form is:

10149 = 3¹ × 17¹ × 199¹

Step-2: 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-3: Factors of 10149

List of positive integer factors of 10149 that divides 10149 without a remainder.

1, 3, 17, 51, 199, 597, 3383

Step-4: Factors of 10164

List of positive integer factors of 10164 that divides 10149 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10149 and 10164. The biggest common factor number is the GCF number.
So the greatest common factor 10149 and 10164 is 3.

Also check out the Least Common Multiple of 10149 and 10164