What is the Greatest Common Factor of 7704 and 7724?

Greatest common factor (GCF) of 7704 and 7724 is 4.

GCF(7704,7724) = 4

We will now calculate the prime factors of 7704 and 7724, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7704 and 7724.

How to find the GCF of 7704 and 7724?

We will first find the prime factorization of 7704 and 7724. After we will calculate the factors of 7704 and 7724 and find the biggest common factor number .

Step-1: Prime Factorization of 7704

Prime factors of 7704 are 2, 3, 107. Prime factorization of 7704 in exponential form is:

7704 = 2³ × 3² × 107¹

Step-2: Prime Factorization of 7724

Prime factors of 7724 are 2, 1931. Prime factorization of 7724 in exponential form is:

7724 = 2² × 1931¹

Step-3: Factors of 7704

List of positive integer factors of 7704 that divides 7704 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 107, 214, 321, 428, 642, 856, 963, 1284, 1926, 2568, 3852

Step-4: Factors of 7724

List of positive integer factors of 7724 that divides 7704 without a remainder.

1, 2, 4, 1931, 3862

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7704 and 7724. The biggest common factor number is the GCF number.
So the greatest common factor 7704 and 7724 is 4.

Also check out the Least Common Multiple of 7704 and 7724