What is the Greatest Common Factor of 38097 and 38114?

Greatest common factor (GCF) of 38097 and 38114 is 17.

GCF(38097,38114) = 17

We will now calculate the prime factors of 38097 and 38114, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38097 and 38114.

How to find the GCF of 38097 and 38114?

We will first find the prime factorization of 38097 and 38114. After we will calculate the factors of 38097 and 38114 and find the biggest common factor number .

Step-1: Prime Factorization of 38097

Prime factors of 38097 are 3, 17, 83. Prime factorization of 38097 in exponential form is:

38097 = 3³ × 17¹ × 83¹

Step-2: Prime Factorization of 38114

Prime factors of 38114 are 2, 17, 19, 59. Prime factorization of 38114 in exponential form is:

38114 = 2¹ × 17¹ × 19¹ × 59¹

Step-3: Factors of 38097

List of positive integer factors of 38097 that divides 38097 without a remainder.

1, 3, 9, 17, 27, 51, 83, 153, 249, 459, 747, 1411, 2241, 4233, 12699

Step-4: Factors of 38114

List of positive integer factors of 38114 that divides 38097 without a remainder.

1, 2, 17, 19, 34, 38, 59, 118, 323, 646, 1003, 1121, 2006, 2242, 19057

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38097 and 38114. The biggest common factor number is the GCF number.
So the greatest common factor 38097 and 38114 is 17.

Also check out the Least Common Multiple of 38097 and 38114