What is the Greatest Common Factor of 38896 and 38909?

Greatest common factor (GCF) of 38896 and 38909 is 13.

GCF(38896,38909) = 13

We will now calculate the prime factors of 38896 and 38909, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38896 and 38909.

How to find the GCF of 38896 and 38909?

We will first find the prime factorization of 38896 and 38909. After we will calculate the factors of 38896 and 38909 and find the biggest common factor number .

Step-1: Prime Factorization of 38896

Prime factors of 38896 are 2, 11, 13, 17. Prime factorization of 38896 in exponential form is:

38896 = 2⁴ × 11¹ × 13¹ × 17¹

Step-2: Prime Factorization of 38909

Prime factors of 38909 are 13, 41, 73. Prime factorization of 38909 in exponential form is:

38909 = 13¹ × 41¹ × 73¹

Step-3: Factors of 38896

List of positive integer factors of 38896 that divides 38896 without a remainder.

1, 2, 4, 8, 11, 13, 16, 17, 22, 26, 34, 44, 52, 68, 88, 104, 136, 143, 176, 187, 208, 221, 272, 286, 374, 442, 572, 748, 884, 1144, 1496, 1768, 2288, 2431, 2992, 3536, 4862, 9724, 19448

Step-4: Factors of 38909

List of positive integer factors of 38909 that divides 38896 without a remainder.

1, 13, 41, 73, 533, 949, 2993

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38896 and 38909. The biggest common factor number is the GCF number.
So the greatest common factor 38896 and 38909 is 13.

Also check out the Least Common Multiple of 38896 and 38909