What is the Greatest Common Factor of 8144 and 8160?

Greatest common factor (GCF) of 8144 and 8160 is 16.

GCF(8144,8160) = 16

We will now calculate the prime factors of 8144 and 8160, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 8144 and 8160.

How to find the GCF of 8144 and 8160?

We will first find the prime factorization of 8144 and 8160. After we will calculate the factors of 8144 and 8160 and find the biggest common factor number .

Step-1: Prime Factorization of 8144

Prime factors of 8144 are 2, 509. Prime factorization of 8144 in exponential form is:

8144 = 2⁴ × 509¹

Step-2: Prime Factorization of 8160

Prime factors of 8160 are 2, 3, 5, 17. Prime factorization of 8160 in exponential form is:

8160 = 2⁵ × 3¹ × 5¹ × 17¹

Step-3: Factors of 8144

List of positive integer factors of 8144 that divides 8144 without a remainder.

1, 2, 4, 8, 16, 509, 1018, 2036, 4072

Step-4: Factors of 8160

List of positive integer factors of 8160 that divides 8144 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 30, 32, 34, 40, 48, 51, 60, 68, 80, 85, 96, 102, 120, 136, 160, 170, 204, 240, 255, 272, 340, 408, 480, 510, 544, 680, 816, 1020, 1360, 1632, 2040, 2720, 4080

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 8144 and 8160. The biggest common factor number is the GCF number.
So the greatest common factor 8144 and 8160 is 16.

Also check out the Least Common Multiple of 8144 and 8160