What is the Greatest Common Factor of 38048 and 38064?

Greatest common factor (GCF) of 38048 and 38064 is 16.

GCF(38048,38064) = 16

We will now calculate the prime factors of 38048 and 38064, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38048 and 38064.

How to find the GCF of 38048 and 38064?

We will first find the prime factorization of 38048 and 38064. After we will calculate the factors of 38048 and 38064 and find the biggest common factor number .

Step-1: Prime Factorization of 38048

Prime factors of 38048 are 2, 29, 41. Prime factorization of 38048 in exponential form is:

38048 = 2⁵ × 29¹ × 41¹

Step-2: Prime Factorization of 38064

Prime factors of 38064 are 2, 3, 13, 61. Prime factorization of 38064 in exponential form is:

38064 = 2⁴ × 3¹ × 13¹ × 61¹

Step-3: Factors of 38048

List of positive integer factors of 38048 that divides 38048 without a remainder.

1, 2, 4, 8, 16, 29, 32, 41, 58, 82, 116, 164, 232, 328, 464, 656, 928, 1189, 1312, 2378, 4756, 9512, 19024

Step-4: Factors of 38064

List of positive integer factors of 38064 that divides 38048 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 61, 78, 104, 122, 156, 183, 208, 244, 312, 366, 488, 624, 732, 793, 976, 1464, 1586, 2379, 2928, 3172, 4758, 6344, 9516, 12688, 19032

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38048 and 38064. The biggest common factor number is the GCF number.
So the greatest common factor 38048 and 38064 is 16.

Also check out the Least Common Multiple of 38048 and 38064