What is the Greatest Common Factor of 7808 and 7814?

Greatest common factor (GCF) of 7808 and 7814 is 2.

GCF(7808,7814) = 2

We will now calculate the prime factors of 7808 and 7814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7808 and 7814.

How to find the GCF of 7808 and 7814?

We will first find the prime factorization of 7808 and 7814. After we will calculate the factors of 7808 and 7814 and find the biggest common factor number .

Step-1: Prime Factorization of 7808

Prime factors of 7808 are 2, 61. Prime factorization of 7808 in exponential form is:

7808 = 2⁷ × 61¹

Step-2: Prime Factorization of 7814

Prime factors of 7814 are 2, 3907. Prime factorization of 7814 in exponential form is:

7814 = 2¹ × 3907¹

Step-3: Factors of 7808

List of positive integer factors of 7808 that divides 7808 without a remainder.

1, 2, 4, 8, 16, 32, 61, 64, 122, 128, 244, 488, 976, 1952, 3904

Step-4: Factors of 7814

List of positive integer factors of 7814 that divides 7808 without a remainder.

1, 2, 3907

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7808 and 7814. The biggest common factor number is the GCF number.
So the greatest common factor 7808 and 7814 is 2.

Also check out the Least Common Multiple of 7808 and 7814