What is the Greatest Common Factor of 38514 and 38528?

Greatest common factor (GCF) of 38514 and 38528 is 14.

GCF(38514,38528) = 14

We will now calculate the prime factors of 38514 and 38528, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38514 and 38528.

How to find the GCF of 38514 and 38528?

We will first find the prime factorization of 38514 and 38528. After we will calculate the factors of 38514 and 38528 and find the biggest common factor number .

Step-1: Prime Factorization of 38514

Prime factors of 38514 are 2, 3, 7, 131. Prime factorization of 38514 in exponential form is:

38514 = 2¹ × 3¹ × 7² × 131¹

Step-2: Prime Factorization of 38528

Prime factors of 38528 are 2, 7, 43. Prime factorization of 38528 in exponential form is:

38528 = 2⁷ × 7¹ × 43¹

Step-3: Factors of 38514

List of positive integer factors of 38514 that divides 38514 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 131, 147, 262, 294, 393, 786, 917, 1834, 2751, 5502, 6419, 12838, 19257

Step-4: Factors of 38528

List of positive integer factors of 38528 that divides 38514 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 43, 56, 64, 86, 112, 128, 172, 224, 301, 344, 448, 602, 688, 896, 1204, 1376, 2408, 2752, 4816, 5504, 9632, 19264

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38514 and 38528. The biggest common factor number is the GCF number.
So the greatest common factor 38514 and 38528 is 14.

Also check out the Least Common Multiple of 38514 and 38528