What is the Greatest Common Factor of 7714 and 7728?

Greatest common factor (GCF) of 7714 and 7728 is 14.

GCF(7714,7728) = 14

We will now calculate the prime factors of 7714 and 7728, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7714 and 7728.

How to find the GCF of 7714 and 7728?

We will first find the prime factorization of 7714 and 7728. After we will calculate the factors of 7714 and 7728 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 7728

Prime factors of 7728 are 2, 3, 7, 23. Prime factorization of 7728 in exponential form is:

7728 = 2⁴ × 3¹ × 7¹ × 23¹

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 7728

List of positive integer factors of 7728 that divides 7714 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 23, 24, 28, 42, 46, 48, 56, 69, 84, 92, 112, 138, 161, 168, 184, 276, 322, 336, 368, 483, 552, 644, 966, 1104, 1288, 1932, 2576, 3864

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7714 and 7728. The biggest common factor number is the GCF number.
So the greatest common factor 7714 and 7728 is 14.

Also check out the Least Common Multiple of 7714 and 7728