What is the Greatest Common Factor of 36294 and 36309?

Greatest common factor (GCF) of 36294 and 36309 is 3.

GCF(36294,36309) = 3

We will now calculate the prime factors of 36294 and 36309, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36294 and 36309.

How to find the GCF of 36294 and 36309?

We will first find the prime factorization of 36294 and 36309. After we will calculate the factors of 36294 and 36309 and find the biggest common factor number .

Step-1: Prime Factorization of 36294

Prime factors of 36294 are 2, 3, 23, 263. Prime factorization of 36294 in exponential form is:

36294 = 2¹ × 3¹ × 23¹ × 263¹

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 36294

List of positive integer factors of 36294 that divides 36294 without a remainder.

1, 2, 3, 6, 23, 46, 69, 138, 263, 526, 789, 1578, 6049, 12098, 18147

Step-4: Factors of 36309

List of positive integer factors of 36309 that divides 36294 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 36294 and 36309. The biggest common factor number is the GCF number.
So the greatest common factor 36294 and 36309 is 3.

Also check out the Least Common Multiple of 36294 and 36309