What is the Greatest Common Factor of 5909 and 5928?

Greatest common factor (GCF) of 5909 and 5928 is 19.

GCF(5909,5928) = 19

We will now calculate the prime factors of 5909 and 5928, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5909 and 5928.

How to find the GCF of 5909 and 5928?

We will first find the prime factorization of 5909 and 5928. After we will calculate the factors of 5909 and 5928 and find the biggest common factor number .

Step-1: Prime Factorization of 5909

Prime factors of 5909 are 19, 311. Prime factorization of 5909 in exponential form is:

5909 = 19¹ × 311¹

Step-2: Prime Factorization of 5928

Prime factors of 5928 are 2, 3, 13, 19. Prime factorization of 5928 in exponential form is:

5928 = 2³ × 3¹ × 13¹ × 19¹

Step-3: Factors of 5909

List of positive integer factors of 5909 that divides 5909 without a remainder.

1, 19, 311

Step-4: Factors of 5928

List of positive integer factors of 5928 that divides 5909 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 19, 24, 26, 38, 39, 52, 57, 76, 78, 104, 114, 152, 156, 228, 247, 312, 456, 494, 741, 988, 1482, 1976, 2964

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5909 and 5928. The biggest common factor number is the GCF number.
So the greatest common factor 5909 and 5928 is 19.

Also check out the Least Common Multiple of 5909 and 5928