What is the Greatest Common Factor of 7697 and 7714?

Greatest common factor (GCF) of 7697 and 7714 is 1.

GCF(7697,7714) = 1

We will now calculate the prime factors of 7697 and 7714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7697 and 7714.

How to find the GCF of 7697 and 7714?

We will first find the prime factorization of 7697 and 7714. After we will calculate the factors of 7697 and 7714 and find the biggest common factor number .

Step-1: Prime Factorization of 7697

Prime factors of 7697 are 43, 179. Prime factorization of 7697 in exponential form is:

7697 = 43¹ × 179¹

Step-2: Prime Factorization of 7714

Prime factors of 7714 are 2, 7, 19, 29. Prime factorization of 7714 in exponential form is:

7714 = 2¹ × 7¹ × 19¹ × 29¹

Step-3: Factors of 7697

List of positive integer factors of 7697 that divides 7697 without a remainder.

1, 43, 179

Step-4: Factors of 7714

List of positive integer factors of 7714 that divides 7697 without a remainder.

1, 2, 7, 14, 19, 29, 38, 58, 133, 203, 266, 406, 551, 1102, 3857

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7697 and 7714. The biggest common factor number is the GCF number.
So the greatest common factor 7697 and 7714 is 1.

Also check out the Least Common Multiple of 7697 and 7714