What is the Greatest Common Factor of 10302 and 10319?

Greatest common factor (GCF) of 10302 and 10319 is 17.

GCF(10302,10319) = 17

We will now calculate the prime factors of 10302 and 10319, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10302 and 10319.

How to find the GCF of 10302 and 10319?

We will first find the prime factorization of 10302 and 10319. After we will calculate the factors of 10302 and 10319 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 10319

Prime factors of 10319 are 17, 607. Prime factorization of 10319 in exponential form is:

10319 = 17¹ × 607¹

Step-3: Factors of 10302

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

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

Step-4: Factors of 10319

List of positive integer factors of 10319 that divides 10302 without a remainder.

1, 17, 607

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10302 and 10319. The biggest common factor number is the GCF number.
So the greatest common factor 10302 and 10319 is 17.

Also check out the Least Common Multiple of 10302 and 10319