What is the Greatest Common Factor of 10285 and 10302?

Greatest common factor (GCF) of 10285 and 10302 is 17.

GCF(10285,10302) = 17

We will now calculate the prime factors of 10285 and 10302, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10285 and 10302.

How to find the GCF of 10285 and 10302?

We will first find the prime factorization of 10285 and 10302. After we will calculate the factors of 10285 and 10302 and find the biggest common factor number .

Step-1: Prime Factorization of 10285

Prime factors of 10285 are 5, 11, 17. Prime factorization of 10285 in exponential form is:

10285 = 5¹ × 11² × 17¹

Step-2: Prime Factorization of 10302

Prime factors of 10302 are 2, 3, 17, 101. Prime factorization of 10302 in exponential form is:

10302 = 2¹ × 3¹ × 17¹ × 101¹

Step-3: Factors of 10285

List of positive integer factors of 10285 that divides 10285 without a remainder.

1, 5, 11, 17, 55, 85, 121, 187, 605, 935, 2057

Step-4: Factors of 10302

List of positive integer factors of 10302 that divides 10285 without a remainder.

1, 2, 3, 6, 17, 34, 51, 101, 102, 202, 303, 606, 1717, 3434, 5151

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10285 and 10302. The biggest common factor number is the GCF number.
So the greatest common factor 10285 and 10302 is 17.

Also check out the Least Common Multiple of 10285 and 10302