What is the Greatest Common Factor of 38896 and 38914?

Greatest common factor (GCF) of 38896 and 38914 is 2.

GCF(38896,38914) = 2

We will now calculate the prime factors of 38896 and 38914, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38896 and 38914.

How to find the GCF of 38896 and 38914?

We will first find the prime factorization of 38896 and 38914. After we will calculate the factors of 38896 and 38914 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 38914

Prime factors of 38914 are 2, 19457. Prime factorization of 38914 in exponential form is:

38914 = 2¹ × 19457¹

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 38914

List of positive integer factors of 38914 that divides 38896 without a remainder.

1, 2, 19457

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38896 and 38914. The biggest common factor number is the GCF number.
So the greatest common factor 38896 and 38914 is 2.

Also check out the Least Common Multiple of 38896 and 38914