What is the Greatest Common Factor of 7700 and 7714?

Greatest common factor (GCF) of 7700 and 7714 is 14.

GCF(7700,7714) = 14

We will now calculate the prime factors of 7700 and 7714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7700 and 7714.

How to find the GCF of 7700 and 7714?

We will first find the prime factorization of 7700 and 7714. After we will calculate the factors of 7700 and 7714 and find the biggest common factor number .

Step-1: Prime Factorization of 7700

Prime factors of 7700 are 2, 5, 7, 11. Prime factorization of 7700 in exponential form is:

7700 = 2² × 5² × 7¹ × 11¹

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 7700

List of positive integer factors of 7700 that divides 7700 without a remainder.

1, 2, 4, 5, 7, 10, 11, 14, 20, 22, 25, 28, 35, 44, 50, 55, 70, 77, 100, 110, 140, 154, 175, 220, 275, 308, 350, 385, 550, 700, 770, 1100, 1540, 1925, 3850

Step-4: Factors of 7714

List of positive integer factors of 7714 that divides 7700 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 7700 and 7714. The biggest common factor number is the GCF number.
So the greatest common factor 7700 and 7714 is 14.

Also check out the Least Common Multiple of 7700 and 7714