What is the Greatest Common Factor of 6144 and 6160?

Greatest common factor (GCF) of 6144 and 6160 is 16.

GCF(6144,6160) = 16

We will now calculate the prime factors of 6144 and 6160, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6144 and 6160.

How to find the GCF of 6144 and 6160?

We will first find the prime factorization of 6144 and 6160. After we will calculate the factors of 6144 and 6160 and find the biggest common factor number .

Step-1: Prime Factorization of 6144

Prime factors of 6144 are 2, 3. Prime factorization of 6144 in exponential form is:

6144 = 2¹¹ × 3¹

Step-2: Prime Factorization of 6160

Prime factors of 6160 are 2, 5, 7, 11. Prime factorization of 6160 in exponential form is:

6160 = 2⁴ × 5¹ × 7¹ × 11¹

Step-3: Factors of 6144

List of positive integer factors of 6144 that divides 6144 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1024, 1536, 2048, 3072

Step-4: Factors of 6160

List of positive integer factors of 6160 that divides 6144 without a remainder.

1, 2, 4, 5, 7, 8, 10, 11, 14, 16, 20, 22, 28, 35, 40, 44, 55, 56, 70, 77, 80, 88, 110, 112, 140, 154, 176, 220, 280, 308, 385, 440, 560, 616, 770, 880, 1232, 1540, 3080

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6144 and 6160. The biggest common factor number is the GCF number.
So the greatest common factor 6144 and 6160 is 16.

Also check out the Least Common Multiple of 6144 and 6160