What is the Greatest Common Factor of 10144 and 10164?

Greatest common factor (GCF) of 10144 and 10164 is 4.

GCF(10144,10164) = 4

We will now calculate the prime factors of 10144 and 10164, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10144 and 10164.

How to find the GCF of 10144 and 10164?

We will first find the prime factorization of 10144 and 10164. After we will calculate the factors of 10144 and 10164 and find the biggest common factor number .

Step-1: Prime Factorization of 10144

Prime factors of 10144 are 2, 317. Prime factorization of 10144 in exponential form is:

10144 = 2⁵ × 317¹

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 10144

List of positive integer factors of 10144 that divides 10144 without a remainder.

1, 2, 4, 8, 16, 32, 317, 634, 1268, 2536, 5072

Step-4: Factors of 10164

List of positive integer factors of 10164 that divides 10144 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 10144 and 10164. The biggest common factor number is the GCF number.
So the greatest common factor 10144 and 10164 is 4.

Also check out the Least Common Multiple of 10144 and 10164