What is the Greatest Common Factor of 28288 and 28305?

Greatest common factor (GCF) of 28288 and 28305 is 17.

GCF(28288,28305) = 17

We will now calculate the prime factors of 28288 and 28305, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 28288 and 28305.

How to find the GCF of 28288 and 28305?

We will first find the prime factorization of 28288 and 28305. After we will calculate the factors of 28288 and 28305 and find the biggest common factor number .

Step-1: Prime Factorization of 28288

Prime factors of 28288 are 2, 13, 17. Prime factorization of 28288 in exponential form is:

28288 = 2⁷ × 13¹ × 17¹

Step-2: Prime Factorization of 28305

Prime factors of 28305 are 3, 5, 17, 37. Prime factorization of 28305 in exponential form is:

28305 = 3² × 5¹ × 17¹ × 37¹

Step-3: Factors of 28288

List of positive integer factors of 28288 that divides 28288 without a remainder.

1, 2, 4, 8, 13, 16, 17, 26, 32, 34, 52, 64, 68, 104, 128, 136, 208, 221, 272, 416, 442, 544, 832, 884, 1088, 1664, 1768, 2176, 3536, 7072, 14144

Step-4: Factors of 28305

List of positive integer factors of 28305 that divides 28288 without a remainder.

1, 3, 5, 9, 15, 17, 37, 45, 51, 85, 111, 153, 185, 255, 333, 555, 629, 765, 1665, 1887, 3145, 5661, 9435

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 28288 and 28305. The biggest common factor number is the GCF number.
So the greatest common factor 28288 and 28305 is 17.

Also check out the Least Common Multiple of 28288 and 28305