What is the Greatest Common Factor of 7714 and 7725?

Greatest common factor (GCF) of 7714 and 7725 is 1.

GCF(7714,7725) = 1

We will now calculate the prime factors of 7714 and 7725, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7714 and 7725.

How to find the GCF of 7714 and 7725?

We will first find the prime factorization of 7714 and 7725. After we will calculate the factors of 7714 and 7725 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 7725

Prime factors of 7725 are 3, 5, 103. Prime factorization of 7725 in exponential form is:

7725 = 3¹ × 5² × 103¹

Step-3: Factors of 7714

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

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

Step-4: Factors of 7725

List of positive integer factors of 7725 that divides 7714 without a remainder.

1, 3, 5, 15, 25, 75, 103, 309, 515, 1545, 2575

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7714 and 7725. The biggest common factor number is the GCF number.
So the greatest common factor 7714 and 7725 is 1.

Also check out the Least Common Multiple of 7714 and 7725