What is the Greatest Common Factor of 32304 and 32319?

Greatest common factor (GCF) of 32304 and 32319 is 3.

GCF(32304,32319) = 3

We will now calculate the prime factors of 32304 and 32319, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32304 and 32319.

How to find the GCF of 32304 and 32319?

We will first find the prime factorization of 32304 and 32319. After we will calculate the factors of 32304 and 32319 and find the biggest common factor number .

Step-1: Prime Factorization of 32304

Prime factors of 32304 are 2, 3, 673. Prime factorization of 32304 in exponential form is:

32304 = 2⁴ × 3¹ × 673¹

Step-2: Prime Factorization of 32319

Prime factors of 32319 are 3, 7, 19. Prime factorization of 32319 in exponential form is:

32319 = 3⁵ × 7¹ × 19¹

Step-3: Factors of 32304

List of positive integer factors of 32304 that divides 32304 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 673, 1346, 2019, 2692, 4038, 5384, 8076, 10768, 16152

Step-4: Factors of 32319

List of positive integer factors of 32319 that divides 32304 without a remainder.

1, 3, 7, 9, 19, 21, 27, 57, 63, 81, 133, 171, 189, 243, 399, 513, 567, 1197, 1539, 1701, 3591, 4617, 10773

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32304 and 32319. The biggest common factor number is the GCF number.
So the greatest common factor 32304 and 32319 is 3.

Also check out the Least Common Multiple of 32304 and 32319