What is the Greatest Common Factor of 36309 and 36314?

Greatest common factor (GCF) of 36309 and 36314 is 1.

GCF(36309,36314) = 1

We will now calculate the prime factors of 36309 and 36314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36309 and 36314.

How to find the GCF of 36309 and 36314?

We will first find the prime factorization of 36309 and 36314. After we will calculate the factors of 36309 and 36314 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 36314

Prime factors of 36314 are 2, 67, 271. Prime factorization of 36314 in exponential form is:

36314 = 2¹ × 67¹ × 271¹

Step-3: Factors of 36309

List of positive integer factors of 36309 that divides 36309 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

Step-4: Factors of 36314

List of positive integer factors of 36314 that divides 36309 without a remainder.

1, 2, 67, 134, 271, 542, 18157

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36309 and 36314. The biggest common factor number is the GCF number.
So the greatest common factor 36309 and 36314 is 1.

Also check out the Least Common Multiple of 36309 and 36314