What is the Greatest Common Factor of 36302 and 36309?

Greatest common factor (GCF) of 36302 and 36309 is 7.

GCF(36302,36309) = 7

We will now calculate the prime factors of 36302 and 36309, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36302 and 36309.

How to find the GCF of 36302 and 36309?

We will first find the prime factorization of 36302 and 36309. After we will calculate the factors of 36302 and 36309 and find the biggest common factor number .

Step-1: Prime Factorization of 36302

Prime factors of 36302 are 2, 7, 2593. Prime factorization of 36302 in exponential form is:

36302 = 2¹ × 7¹ × 2593¹

Step-2: Prime Factorization of 36309

Prime factors of 36309 are 3, 7, 13, 19. Prime factorization of 36309 in exponential form is:

36309 = 3¹ × 7² × 13¹ × 19¹

Step-3: Factors of 36302

List of positive integer factors of 36302 that divides 36302 without a remainder.

1, 2, 7, 14, 2593, 5186, 18151

Step-4: Factors of 36309

List of positive integer factors of 36309 that divides 36302 without a remainder.

1, 3, 7, 13, 19, 21, 39, 49, 57, 91, 133, 147, 247, 273, 399, 637, 741, 931, 1729, 1911, 2793, 5187, 12103

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36302 and 36309. The biggest common factor number is the GCF number.
So the greatest common factor 36302 and 36309 is 7.

Also check out the Least Common Multiple of 36302 and 36309