What is the Greatest Common Factor of 38506 and 38514?

Greatest common factor (GCF) of 38506 and 38514 is 2.

GCF(38506,38514) = 2

We will now calculate the prime factors of 38506 and 38514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38506 and 38514.

How to find the GCF of 38506 and 38514?

We will first find the prime factorization of 38506 and 38514. After we will calculate the factors of 38506 and 38514 and find the biggest common factor number .

Step-1: Prime Factorization of 38506

Prime factors of 38506 are 2, 13, 1481. Prime factorization of 38506 in exponential form is:

38506 = 2¹ × 13¹ × 1481¹

Step-2: 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-3: Factors of 38506

List of positive integer factors of 38506 that divides 38506 without a remainder.

1, 2, 13, 26, 1481, 2962, 19253

Step-4: Factors of 38514

List of positive integer factors of 38514 that divides 38506 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38506 and 38514. The biggest common factor number is the GCF number.
So the greatest common factor 38506 and 38514 is 2.

Also check out the Least Common Multiple of 38506 and 38514